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In this dissertation, we study nonlocal quantum field theories obtained by delocalizing the fields in the interaction terms of some local Lagrangian. The delocalization kernels in momentum space are exponentials of entire functions, thus no additional mass poles are introduced, but they ensure UV finiteness of loop integrals of Feynman diagrams. The transition matrix is defined in the Euclidean regime, followed by analytic continuation of the external momenta. Because of the delocalization kernels, manipulations valid in local theories are prohibited in the nonlocal theories, including Wick rotation and dispersion relation. We study the analyticity structure of the transition matrix of such theories at the perturbative level, using the Landau equations. The result shows that singularities that occur in local theories are also present in the nonlocal theories, except for singularities of the second type. The Cutkosky rule is then derived using Cutkosky's original argument, and the unitarity condition follows as an application of the rule. We then quantify the acausality present in such nonlocal theories using the Bogoliubov causality condition (BCC). First we study the acausality of the effective propagator, which is shown to be exponentially suppressed for large space-time separation. Mellin transform is introduced to help find the asymptotic behavior of acausality. Next we prove that in local theories, for each diagram, the BCC equation amounts to a chain of retarded propagator between two vertices; while in nonlocal theories, the chain consists of $\tilde\Delta_R$, which is the retarded propagator delocalized by the nonlocal kernel and is therefore no longer causal. The acausal amplitudes are then integrated over wave packets to make experimental predictions. We show that for a nonlocality scale of order Plank's length, the acausality will be experimentally immeasurable. Along the way, by extending the BCC to unitarity equations, we show that the theory defined directly in Minkowksi space is not unitary. This reaffirms that the theory has to be defined in the Euclidean regime and then analytically continued.

In arXiv:1907.07688 Balthazar, Rodriguez and Yin (BRY) computed the one instanton contribution to the two point scattering amplitude in two dimensional string theory to first subleading order in the string coupling. Their analysis left undetermined two constants due to divergences in the integration over world-sheet variables, but they were fixed by numerically comparing the result with that of the dual matrix model. If we consider n-point scattering amplitudes to the same order, there are actually four undetermined constants in the world-sheet approach. We show that using string field theory we can get finite unambiguous values of all of these constants, and we explicitly compute three of these four constants. Two of the three constants determined this way agree with the numerical result of BRY within the accuracy of numerical analysis, but the third constant seems to differ by 1/2. We also discuss a shortcut to determining the fourth constant if we assume the equality of the quantum corrected D-instanton action and the action of the matrix model instanton. This also agrees with the numerical result of BRY. Note added: The apparent discrepancy in the third constant has been resolved in arXiv:2210.11473., Comment: LaTeX file, 100 pages, This paper reports an apparent mismatch between string theory and matrix model results, hoping that someone will find an error; v2: The apparent mismatch has been resolved in arXiv:2210.11473

D-instanton amplitudes suffer from various infrared divergences associated with tachyonic or massless open string modes, leading to ambiguous contribution to string amplitudes. It has been shown previously that string field theory can resolve these ambiguities and lead to unambiguous expressions for D-instanton contributions to string amplitudes, except for an overall normalization constant that remains undetermined. In this paper we show that string field theory, together with the world-sheet description of the amplitudes, can also fix this normalization constant. We apply our analysis to the special case of two dimensional string theory, obtaining results in agreement with the matrix model results obtained by Balthazar, Rodriguez and Yin., LaTeX file, 20 pages; v2: minor clarifications and references added

A large body of work over several decades indicates that, in the presence of gravitational interactions, there is loss of localization resolution within a fundamental ( $\sim$ Planck) length scale $\ell$. We develop a general formalism based on wavelet decomposition of fields that takes this UV `opaqueness' into account in a natural and mathematically well-defined manner. This is done by requiring fields in a local Lagrangian to be expandable in only the scaling parts of a (complete or, in a more general version, partial) wavelet Multi-Resolution Analysis. This delocalizes the interactions, now mediated through the opaque regions, inside which they are rapidly decaying. The opaque regions themselves are capable of discrete excitations of $\sim 1/\ell$ spacing. The resulting effective Feynman rules, which give UV regulated and (perturbatively) unitary physical amplitudes, resemble those of string field theory., Comment: 22 pages, 2 figures, minor comments added, typos corrected, published version

In Double Field Theory, the mass-squared of doubled fields associated with bosonic closed string states is proportional to $N_L+N_R-2$. Massless states are therefore not only the graviton, anti-symmetric, and dilaton fields with $(N_L=1, N_R=1)$ such theory is focused on, but also the symmetric traceless tensor and the vector field relative to the states $(N_L=2, N_R=0)$ and $(N_L=0, N_R=2)$ which are massive in the lower-dimensional non-compactified space. While they are not even physical in the absence of compact dimensions, they provide a sample of states for which both momenta and winding numbers are non-vanishing, differently from the states $(N_L=1, N_R=1)$. A quadratic action is therefore here built for the corresponding doubled fields. It results that its gauge invariance under the linearized double diffeomorphisms is based on a generalization of the usual weak constraint, giving rise to an extra mass term for the symmetric traceless tensor field, not otherwise detectable: this can be interpreted as a mere stringy effect in target space due to the simultaneous presence of momenta and windings. Furthermore, in the context of the generalized metric formulation, a non-linear extension of the gauge transformations is defined involving the constraint extended from the weak constraint that can be uniquely defined in triple products of fields. Finally, we show that the above mentioned stringy effect does not appear in the case of only one compact doubled space dimension., 19 pages, minor changes, reference changed

We continue the study of positive geometries underlying the {\it Grassmannian string integrals}, which are a class of "stringy canonical forms", or stringy integrals, over the positive Grassmannian mod torus action, $G_+(k,n)/T$. The leading order of any such stringy integral is given by the canonical function of a polytope, which can be obtained using the Minkowski sum of the Newton polytopes for the regulators of the integral, or equivalently given by the so-called scattering-equation map. The canonical function of the polytopes for Grassmannian string integrals, or the volume of their dual polytopes, is also known as the generalized bi-adjoint $\phi^3$ amplitudes. We compute all the linear functions for the facets which cut out the polytope for all cases up to $n=9$, with up to k=4 and their parity conjugate cases. The main novelty of our computation is that we present these facets in a manifestly gauge-invariant and cyclic way, and identify the boundary configurations of $G_+(k,n)/T$ corresponding to these facets, which have nice geometric interpretations in terms of $n$ points in $(k{-}1)$-dimensional space. All the facets and configurations we discovered up to $n=9$ directly generalize to all $n$, although new types are still needed for higher $n$., Comment: 34 pages+ appendices, lots of figures, with typo fixed. Ancilliary files for all the facets up to $k=3$, $n=10$ and $k=4$, $n=9$, as well as ampltitudes up to $n=8$ are included with the submission

The following notes derive from review lectures on closed string field theory given at the Galileo Galilei Institute for Theoretical Physics in March 2019., Comment: v3: 54 pages, 19 figures. Redrawn figures with increased resolution; new appendix; other improvements as requested by referee

We study super-Chern-Simons theory on a generic supermanifold. After a self-contained review of integration on supermanifolds, the complexes of forms (superforms, pseudo-forms and integral forms) and the extended Cartan calculus are discussed. We then introduce Picture Changing Operators. We provide several examples of computation of PCO's acting on different type of forms. We illustrate also the action of the $\eta$ operator, crucial ingredient to define the interactions of super Chern-Simons theory. Then, we discuss the action for super Chern-Simons theory on any supermanifold, first in the factorized form (3-form $\times$ PCO) and then, we consider the most general expression. The latter is written in term of psuedo-forms containing an infinite number of components. We show that the free equations of motion reduce to the usual Chern-Simons equations yielding the proof of the equivalence between the formulations at different pictures of the same theory. Finally, we discuss the interaction terms. They require a suitable definition in order to take into account the picture number. That implies the construction of a 2-product which is not associative that inherits an $A_\infty$ algebra structure. That shares several similarities with a recent construction of a super string field theory action by Erler, Konopka and Sachs., Comment: 59 pages, Latex2e

We propose a transformation between the off-shell field variables of Witten's open bosonic string field theory and the traditional lightcone string field theory of Kaku and Kikkawa, based on Mandelstam's interacting string picture. This is accomplished by deforming the Witten vertex into lightcone cubic and quartic vertices, followed by integrating out the ghost and lightcone oscillator excitations from the string field. Surprisingly, the last step does not alter the cubic and quartic interactions and does not generate effective vertices, and leads precisely to Kaku and Kikkawa's lightcone string field theory., 74 pages, 23 figures. Added appendix on the lightcone SFT action. Simplified discussion of the field transformation and the singular nature of lightcone gauge in generic SFTs, which has been called the "soft string problem."

This is the second paper of a series of three. We construct effective open-closed superstring couplings by classically integrating out massive fields from open superstring field theories coupled to an elementary gauge invariant tadpole proportional to an on-shell closed string state in both large and small Hilbert spaces, in the NS sector. This source term is well known in the WZW formulation and by explicitly performing a novel large Hilbert space perturbation theory we are able to characterize the first orders of the vacuum shift solution, its obstructions and the non-trivial open-closed effective couplings in closed form. With the aim of getting all order results, we also construct a new observable in the A∞ theory in the small Hilbert space which correctly provides a gauge invariant coupling to physical closed strings and which descends from the WZW open-closed coupling upon partial gauge fixing and field redefinition. Armed with this new A∞ observable we use tensor co-algebra techniques to efficiently package the whole perturbation theory necessary for computing the effective action and we give all order results for the open-closed effective couplings in the small Hilbert space., Journal of High Energy Physics, 2021 (9), ISSN:1126-6708, ISSN:1029-8479

We investigate the non-perturbative regimes in the class of non-Abelian theories that have been proposed as an ultraviolet completion of 4-D Quantum Field Theory (QFT) generalizing the kinetic energy operators to an infinite series of higher-order derivatives inspired by string field theory. We prove that, at the non-perturbative level, the physical spectrum of the theory is actually corrected by the “infinite number of derivatives” present in the action. We derive a set of Dyson-Schwinger equations in differential form, for correlation functions till two-points, the solution for which are known in the local theory. We obtain that just like in the local theory, the non-local counterpart displays a mass gap, depending also on the mass scale of non-locality, and show that it is damped in the deep UV asymptotically. We point out some possible implications of our result in particle physics and cosmology and discuss aspects of non-local QCD-like scenarios.

In perturbative amplitudes in quantum field theory and string field theory, Cutkosky rule expresses the anti-hermitian part of a Feynman diagram in terms of sum over all its cut diagrams, and this in turn is used to prove unitarity of the theory. For D-instanton contribution to a string theory amplitude, the cutting rule needed for the proof of unitarity is somewhat different; we need to sum over only those cut diagrams for which all the world-sheet boundaries ending on some particular D-instanton lie on the same side of the cut. By working with the closed string effective action, obtained after integrating out the open string modes, we prove that the D-instanton amplitudes actually satisfy these cutting rules, provided the effective action is real. The violation of unitarity in the closed string sector of two dimensional string theory can be traced to the failure of this reality condition. In the critical superstring theory, multi-instanton and multi anti-instanton amplitudes satisfy the reality condition. Contribution to the amplitudes from the instanton anti-instanton sector satisfies the reality condition if we make a specific choice of integration cycle over the configuration space of string fields, whereas contribution due to the non-BPS D-instantons will need to either vanish or have an overall real normalization in order for it to give real contribution. We use Picard-Lefschetz theory to argue that these conditions are indeed satisfied in superstring theories., LaTeX file; 94 pages

The quantum Batalian-Vilkovisky master action for closed string field theory consists of kinetic term and infinite number of interaction terms. The interaction strengths (coupling constants) are given by integrating the off-shell string measure over the distinct string diagrams describing the elementary interactions of the closed strings. In the first paper of this series, it was shown that the string diagrams describing the elementary interactions can be characterized using the Riemann surfaces endowed with the hyperbolic metric with constant curvature −1. In this paper, we construct the off-shell bosonic-string measure as a function of the Fenchel-Nielsen coordinates of the Teichmüller space of hyperbolic Riemann surfaces. We also describe an explicit procedure for integrating the off-shell string measure over the region inside the moduli space corresponding to the elementary interactions of the closed strings.

We point out that the one-particle-irreducible vacuum correlation functions of a QFT are the structure constants of an L ∞-algebra, whose Jacobi identities hold whenever there are no local gauge anomalies. The LSZ prescription for S-matrix elements is identified as an instance of the “minimal model theorem” of L ∞-algebras. This generalises the algebraic structure of closed string field theory to arbitrary QFTs with a mass gap and leads to recursion relations for amplitudes (albeit ones only immediately useful at tree-level, where they reduce to Berends-Giele-style relations as shown in [1]).

Motivated by the appearance of associativity anomalies in the context of superstring field theory, we give a generalized solution built from boundary condition changing operators which can be associated to a generic tachyon vacuum in the $KBc$ subalgebra of the Okawa form. We articulate sufficient conditions on the choice of tachyon vacuum to ensure that ambiguous products do not appear in the equations of motion., Comment: v3: 19 pages. Corrected error in (2.12)

We show that boundary string field theory realizes the minimal model of open string field theory. More precisely, we observe that the expansion of the (co)homological vector field, $Q$ of boundary string field theory in the cohomology of its linear part reproduces the S-matrices of perturbative string theory. In mathematical terms, boundary string field theory realizes the minimal model map of the cohomological perturbation lemma., 18 pages, 3 figures. Majorly revised version. Introductory section added, figure added, figure 2 replaced, typos corrected. Accepted for puplication in JHEP

It is shown that the recently introduced positivity and causality preserving string-local quantum field theory (SLFT) resolves most No-Go situations in higher spin problems. This includes in particular the Velo–Zwanziger causality problem which turns out to be related in an interesting way to the solution of zero mass Weinberg–Witten issue. In contrast to the indefinite metric and ghosts of gauge theory, SLFT uses only positivity-respecting physical degrees of freedom. The result is a fully Lorentz-covariant and causal string field theory in which light- or space-like linear strings transform covariant under Lorentz transformation.The cooperation of causality and quantum positivity in the presence of interacting s≥1 particles leads to remarkable conceptual changes. It turns out that the presence of H-selfinteractions in the Higgs model is not the result of SSB on a postulated Mexican hat potential, but solely the consequence of the implementation of positivity and causality. These principles (and not the imposed gauge symmetry) account also for the Lie-algebra structure of the leading contributions of selfinteracting vector mesons.Second order consistency of selfinteracting vector mesons in SLFT requires the presence of H-particles; this, and not SSB, is the raison d'être for H.The basic conceptual and calculational tool of SLFT is the S-matrix. Its string-independence is a powerful restriction which determines the form of interaction densities in terms of the model-defining particle content and plays a fundamental role in the construction of pl observables and sl interpolating fields.

We obtain the subleading soft theorem for a generic theory of quantum gravity, for arbitrary number of soft photons and gravitons and for arbitrary number of finite energy particles with arbitrary mass and spin when all the soft particles are soft in the same rate. This result is valid at tree level for spacetime dimensions equal to four and five and to all loops in spacetime dimensions greater than five. We verify that in classical limit low energy photon and graviton radiation decouple from each other., Comment: 55 pages, 14 figures, covariantization in photon background improved, appendix-B added

We compute six-point string amplitudes for the scattering of one closed string Ramond-Ramond state, two tachyons, and two gauge fields in the worldvolume of D-brane-anti-D-brane systems in the Type II superstring theories. From the resulting S-matrix elements, we read off the precise form of the couplings, including their exact numerical coefficients, of two tachyons and two gauge fields in the corresponding highly symmetric effective field theory (EFT) Lagrangian in the worldvolume of D-brane-Anti-D-brane to all orders in $\alpha'$, which modify and complete previous proposals. We verify that the EFT reproduces the infinite collection of stringy gauge field singularities in dual channels. Inspired by interesting similarities between the all-order highly symmetric EFTs and holographic duals of Vasiliev's higher spin gravities \`a l\`a Nilsson and Vasiliev, we make a proposal for tensionless limits of D-brane-anti-D-brane systems., Comment: V4: clarifications added. Published version in JHEP

On the basis of the intimate relation between Nambu dynamics and the hydrodynamics, the hydrodynamics on a non-commutative space (obtained by the quantization of space), proposed by Nambu in his last work, is formulated as ``hydrodynamics of granular material''. In Part 1, the quantization of space is done by Moyal product, and the hydrodynamic simulation is performed for the so obtained two dimensional fluid, which flows inside a canal with an obstacle. The obtained results differ between two cases in which the size of a fluid particle is zero and finite. The difference seems to come from the behavior of vortices generated by an obstacle. In Part 2 of quantization, considering vortex as a string, two models are examined; one is the ``hybrid model'' in which vortices interact with each other by exchanging Kalb-Ramond fields (a generalization of stream functions), and the other is the more general ``string field theory'' in which Kalb-Ramond field is one of the excitation mode of string oscillations. In the string field theory, Altarelli-Parisi type evolution equation is introduced. It is expected to describe the response of distribution function of vortex inside a turbulence, when the energy scale is changed. The behaviour of viscosity differs in the string theory, being compared with the particle theory, so that Landau theory of fluid to introduce viscosity may be modified. In conclusion, the hydrodynamics and the string theory are almost identical theories. It should be noted, however, that the string theory to reproduce a given hydrodynamics is not a usual string theory., 15 pages, 7 figures

Using the level truncation method, we construct numerical solutions, which are twist even and SU(1,1) singlet, in the theory around the Takahashi-Tanimoto identity-based solution (TT solution) with a real parameter $a$ in the framework of bosonic open string field theory. We find solutions corresponding to "double brane" and "ghost brane" solutions which were constructed by Kudrna and Schnabl in the conventional theory around the perturbative vacuum. Our solutions show somewhat similar $a$-dependence to tachyon vacuum and single brane solutions, which we found in the earlier works. In this sense, we might be able to expect that they are consistent with the conventional interpretation of $a$-dependence of the TT solution. We observe that numerical complex solutions at low levels become real ones at higher levels for some region of the parameter $a$. However, these real solutions do not so improve interpretation for double brane., Comment: 24 figures

We begin developing tools to compute off-shell string amplitudes with the recently proposed hyperbolic string vertices of Costello and Zwiebach. Exploiting the relation between a boundary value problem for Liouville's equation and a monodromy problem for a Fuchsian equation, we construct the local coordinates around the punctures for the generalized hyperbolic three-string vertex and investigate their various limits. This vertex corresponds to the general pants diagram with three boundary geodesics of unequal lengths. We derive the conservation laws associated with such vertex and perform sample computations. We note the relevance of our construction to the calculations of the higher-order string vertices using the pants decomposition of hyperbolic Riemann surfaces., 37 pages, 6 figures, v2: minor typos corrected, version published in JHEP

The open string field theory of Witten (SFT) has a close formal similarity with Chern-Simons theory in three dimensions. This similarity is due to the fact that the former theory has concepts corresponding to forms, exterior derivative, wedge product and integration over the manifold. In this paper, we introduce the interior product and the Lie derivative in the $KBc$ subsector of SFT. The interior product in SFT is specified by a two-component "tangent vector" and lowers the ghost number by one (like the ordinary interior product maps a $p$-form to $(p-1)$-form). The Lie derivative in SFT is defined as the anti-commutator of the interior product and the BRST operator. The important property of these two operations is that they respect the $KBc$ algebra. Deforming the original $(K,B,c)$ by using the Lie derivative, we can consider an infinite copies of the $KBc$ algebra, which we call the $KBc$ manifold. As an application, we construct the Wilson line on the manifold, which could play a role in reproducing degenerate fluctuation modes around a multi-brane solution., Comment: 22 pages, 1 figure. version to appear in JHEP

We argue that String Theory and Loop Quantum Gravity can be thought of as describing different regimes of a single unified theory of quantum gravity. LQG can be thought of as providing the pre-geometric exoskeleton out of which macroscopic geometry emerges and String Theory then becomes the effective theory which describes the dynamics of that exoskeleton. The core of the argument rests on the claim that the Nambu-Goto action of String Theory can be viewed as the expectation value of the LQG area operator evaluated on the string worldsheet. A concrete result is that the string tension of String Theory and the Barbero-Immirzi parameter of LQG turn out to be proportional to each other.

This is the first of a series of three papers on open string field theories based on Witten star product deformed with a gauge invariant open/closed coupling. This de- formation is a tree-level tadpole which destabilizes the initial perturbative vacuum. We discuss the existence of vacuum-shift solutions which cancel the tadpole and represent a new configuration where the initial D-brane system has adapted to the change in the closed string background. As an example we consider the bulk deformation which changes the compactification radius and, to first order in the deformation, we reproduce the shift in the mass of the open string KK modes from the new kinetic operator after the vacuum shift. We also discuss the possibility of taming closed string degenerations with the open string propagator in the simplest amplitude corresponding to two closed strings off a disk., Journal of High Energy Physics, 2021 (9), ISSN:1126-6708, ISSN:1029-8479

We study multi-boundary correlators in 2d Witten-Kontsevich topological gravity. We present a proof of the loop equations obeyed by the correlators. While the loop equations were derived a long time ago, our proof is fully explicit in the presence of general couplings $t_k$. We clarify all the details, in particular the treatment of the genus zero part of the one-boundary correlator. The loop equations are verified by several new examples, including the correlators of Jackiw-Teitelboim gravity in the genus expansion and the exact correlators in the Airy case. We also discuss the free boson/fermion representation of the correlators and compare it with the formulation of Marolf and Maxfield and the string field theory of Ishibashi and Kawai. We find similarities but also some differences., Comment: 33 pages, v2: some explanations added, published version

In this paper, which is the last of a series including [1, 2] we first verify that the two open-closed effective potentials derived in the previous paper from the WZW theory in the large Hilbert space and the A(infinity) theory in the small Hilbert space have the same vacuum structure. In particular, we show that mass-term deformations given by the effective (open)(2)-closed couplings are the same, provided the effective tadpole is vanishing to first order in the closed string deformation. We show that this condition is always realized when the worldsheet BCFT enjoys a global N = 2 superconformal symmetry and the deforming closed string belongs to the chiral ring in both the holomorphic and anti-holomorphic sector. In this case it is possible to explicitly evaluate the mass deformation by localizing the SFT Feynman diagrams to the boundary of world-sheet moduli space, reducing the amplitude to a simple open string two-point function. As a non-trivial check of our construction we couple a constant Kalb-Ramond closed string state to the OSFT on the D3-D( -1) system and we show that half of the bosonic blowing-up moduli become tachyonic, making the system condense to a bound state whose binding energy we compute exactly to second order in the closed string deformation, finding agreement with the literature., Journal of High Energy Physics, 2021 (9), ISSN:1126-6708, ISSN:1029-8479

Recent results of A. Sen on quantum field theory models with self-dual field strengths use string field theory as a starting point. In the present work, we show that combining string field theory and supergeometry we can provide a constructive method for all these models, for any superspace representation and for any given background. The analysis is based on the new concept of pseudoform, emerging in supergeometry, which opens a new page in quantum field theory and, in particular, in supergravity. The present work deals with an explicit example, the case of the N=1 chiral boson supermultiplet in d=2.

In this paper, we analyze the inflationary cosmology using string field theory. This is done by using the zero level contribution from string field theory, which is a non-local tachyonic action. We will use the non-local Friedmann equations for this model based on string field theory, and calculate the slow-roll parameters for this model. We will then explicitly obtain the scalar and tensorial power spectrum, their related indices, and the tensor-to-scalar ratio for this model. Finally, we use cosmological data from Planck 2013 to 2018 to constrain the free parameters in this model and find that string field theory is compatible with them., 15 pages, 4 figures, 1 table; it has been accepted in Nuclear Physics B (NPB)

We study particle theories that have a tower of worldline internal degrees of freedom. Such a theory can arise when the worldsheet of closed strings is dimensionally reduced to a worldline, in which case the tower is infinite with regularly spaced masses. But our discussion is significantly more general than this, and there is scope to consider all kinds of internal degrees of freedom carried by the propagating particle. For example it is possible to consider towers corresponding to other geometries, or towers with no obvious geometric interpretation that still yield a modular invariant theory. Truncated towers generate non-local particle theories that share with string theory the property of having a Gross-Mende-like saddle point in their amplitudes. This provides a novel framework for constructing exotic theories which may have desirable properties such as finiteness and modular invariance., Typos corrected

We treat RR flux backgrounds of type II string theory in the framework of closed superstring field theory based on the NSR formalism, focusing on two examples: (1) the pp-wave background supported by 5-form flux, and (2) $AdS_3\times S^3\times M_4$ supported by mixed 3-form fluxes. In both cases, we analyze the classical string field solution perturbatively, and compute the correction to the dispersion relation of string states to quadratic order in the RR flux. In the first example, our result is in a delicate way consistent with that obtained from lightcone quantization of the Green-Schwarz string. In the second example, we will obtain numerically the mass corrections to pulsating type IIB strings in $AdS_3\times S^3\times M_4$. Our results, valid at finite $AdS$ radius, agree with previously known answers in the semiclassical limit and in the BMN limit respectively., 49 pages, 3 figures, 1 table, v2: comments on references added, references added, typos corrected, v3: minor corrections, v4: comments in section 2.1 added

We discuss the symmetry factors of Feynman diagrams of scalar field theories with polynomial potential. After giving a concise general formula for them, we present an elementary and direct proof that when computing scattering amplitudes using the homological perturbation lemma, each contributing Feynman diagram is indeed included with the correct symmetry factor., Comment: 20 pages

We study generic properties of string theory effective actions obtained by classically integrating out massive excitations from string field theories based on cyclic homotopy algebras of $A_\infty$ or $L_\infty$ type. We construct observables in the UV theory and we discuss their fate after integration-out. Furthermore, we discuss how to compose two subsequent integrations of degrees of freedom (horizontal composition) and how to integrate out degrees of freedom after deforming the UV theory with a new consistent interaction (vertical decomposition). We then apply our general results to the open bosonic string using Witten's open string field theory. There we show how the horizontal composition can be used to systematically integrate out the Nakanishi-Lautrup field from the set of massless excitations, ending with a non-abelian $A_\infty$-gauge theory for just the open string gluon. Moreover we show how the vertical decomposition can be used to construct effective open-closed couplings by deforming Witten OSFT with a tadpole given by the Ellwood invariant. Also, we discuss how the effective theory controls the possibility of removing the tadpole in the microscopic theory, giving a new framework for studying D-branes deformations induced by changes in the closed string background., 85 pages

We construct a family of hyperbolic string vertices in the oriented open-closed string field theory, generalizing the recent result on hyperbolic closed string vertices by Costello and Zwiebach. The vertices are described by certain bordered hyperbolic surfaces and we explain relevant collar theorems which provide restrictions on the systolic conditions for the hyperbolic vertices. We also give explicit descriptions of the vertices for all zero and one-dimensional moduli spaces., Comment: 42 pages, 15 figures

In a linear dilaton background, it has been argued that an unstable D-brane can decay to the tachyon vacuum without leaving behind a remnant of tachyon matter. Here we address the question of how the D-brane can decay to the tachyon vacuum when the tachyon vacuum does not support physical fluctuations. Using the formalism of open string field theory, we find that the tachyon vacuum {\it can} support fluctuations provided they are "hidden" as nonperturbative effects behind a pure gauge asymptotic series., Comment: 41 pages, 12 figures

In a recent paper, Balthazar, Rodriguez and Yin found some remarkable agreement between the results of c=1 matrix model and D-instanton corrections in two dimensional string theory. Their analysis left undetermined two constants in the string theory computation which had to be fixed by comparing the results with the matrix model results. One of these constants is affected by possible renormalization of the D-instanton action that needs to be computed separately. In this paper we fix the other constant by reformulating the world-sheet analysis in the language of string field theory., Comment: LaTeX file, 15 pages; v2: references added

Based on the level truncation scheme, we develop a new numerical method to evaluate the tachyon vacuum solution in the Schnabl gauge up to level $L=24$. We confirm the prediction that the energy associated to this numerical solution has a local minimum at level $L=12$. Extrapolating the energy data of $L \leq 24$ to infinite level, we observe that the energy goes towards the analytical value $-1$, nevertheless the precision of the extrapolation is lower than in the Siegel gauge. Furthermore, we analyze the Ellwood invariant and show that its value converges monotonically towards the expected analytical result. We also study the tachyon vacuum expectation value (vev) and some other coefficients of the solution. Finally, some consistency checks of the solution are performed, and we briefly discuss the search for other Schnabl gauge numerical solutions., 31 pages, 3 figures, appendix A added

We construct a quadratic curvature theory of gravity whose graviton propagator around the Minkowski background respects wordline inversion symmetry, the particle approximation to modular invariance in string theory. This symmetry automatically yields a corresponding gravitational theory that is nonlocal, with the action containing infinite order differential operators. As a consequence, despite being a higher order derivative theory, it is ghost-free and has no degrees of freedom besides the massless spin-$2$ graviton of Einstein's general relativity. By working in the linearised regime we show that the point-like singularities that afflict the (local) Einstein's theory are smeared out., 16 pages, 1 figure

We consider the off-shell momentum space Green's functions in closed superstring field theory. Recently in arXiv:1810.07197, the off-shell Green's functions -- after explicitly removing contributions of massless states -- have been shown to be analytic on a domain (to be called the LES domain) in complex external momenta variables. Analyticity of off-shell Green's functions in local QFTs without massless states in the primitive domain is a well-known result. Using complex Lorentz transformations and Bochner's theorem allow to extend the LES domain to a larger subset of the primitive domain. For the 2-, 3- and 4-point functions, the full primitive domain is recovered. For the 5-point function, we are not able to obtain the full primitive domain analytically, only a large part of it is recovered. While this problem arises also for higher-point functions, it is expected to be only a technical issue., Comment: 27 pages, Version accepted in JHEP

D-instanton world-volume theory has open string zero modes describing collective coordinates of the instanton. The usual perturbative amplitudes in the D-instanton background suffer from infra-red divergences due to the presence of these zero modes, and the usual approach of analytic continuation in momenta does not work since all open string states on a D-instanton carry strictly zero momentum. String field theory is well-suited for tackling these issues. However we find a new subtlety due to the existence of additional zero modes in the ghost sector. This causes a breakdown of the Siegel gauge, but a different gauge fixing consistent with the BV formalism renders the perturbation theory finite and unambiguous. At each order, this produces extra contribution to the amplitude besides what is obtained from integration over the moduli space of Riemann surfaces., Comment: LaTeX file, 24 pages; v2: expanded discussion on ghost zero modes

This book gives a modern presentation of modular operands and their role in string field theory. The authors aim to outline the arguments from the perspective of homotopy algebras and their operadic origin. Part I reviews string field theory from the point of view of homotopy algebras, including A-infinity algebras, loop homotopy (quantum L-infinity) and IBL-infinity algebras governing its structure. Within this framework, the covariant construction of a string field theory naturally emerges as composition of two morphisms of particular odd modular operads. This part is intended primarily for researchers and graduate students who are interested in applications of higher algebraic structures to strings and quantum field theory. Part II contains a comprehensive treatment of the mathematical background on operads and homotopy algebras in a broader context, which should appeal also to mathematicians who are not familiar with string theory.

Unlike conformal boundary conditions, conformal defects of Virasoro minimal models lack classification. Alternatively to the defect perturbation theory and the truncated conformal space approach, we employ open string field theory (OSFT) techniques to explore the space of conformal defects. We illustrate the method by an analysis of OSFT around the background associated to the $(1,2)$ topological defect in diagonal unitary minimal models. Numerical analysis of OSFT equations of motion leads to an identification of a nice family of solutions, recovering the picture of infrared fixed points due to Kormos, Runkel and Watts. In particular, we find a continuum of solutions in the Ising model case and 6 solutions for other minimal models. OSFT provides us with numerical estimates of the g-function and other coefficients of the boundary state., Comment: 37 pages, 8 figures, 6 tables, v2: minor typos corrected

In this work, we investigate the bosonic chiral string in the sectorized interpretation, computing its spectrum, kinetic action and $3$-point amplitudes. As expected, the bosonic ambitwistor string is recovered in the tensionless limit. We also consider an extension of the bosonic model with current algebras. In that case, we compute the effective action and show that it is essentially the same as the action of the mass-deformed $(DF)^{2}$ theory found by Johansson and Nohle. Aspects which might seem somewhat contrived in the original construction --- such as the inclusion of a scalar transforming in some real representation of the gauge group --- are shown to follow very naturally from the worldsheet formulation of the theory., Comment: 24 pages + appendix; v2: improved notation; v3: minor modifications, published version

We consider structure constants of single-trace operators at strong coupling in planar $\mathcal{N}=4$ SYM theory using the hexagon formalism. We concentrate on heavy-heavy-light correlators where the heavy operators are BMN operators, with large R-charges and finite anomalous dimensions, and the light one is a finite-charge chiral primary operator. They describe the couplings between two highly boosted strings and a supergravity mode in the bulk dual. In the hexagon framework, two sums over virtual magnons are needed to bind the hexagons together around the light operator. We evaluate these sums explicitly at strong coupling, for a certain choice of BMN operators, and show that they factorise into a ratio of Gamma functions and a simple stringy prefactor. The former originates from giant mirror magnons scanning the AdS geometry while the latter stems from small fluctuations around the BMN vacuum. The resulting structure constants have poles at positions where an enhanced mixing with double-trace operators is expected and zeros whenever the process is forbidden by supersymmetry. We also discuss the transition to the classical regime, when the length of the light operator scales like the string tension, where we observe similitudes with the Neumann coefficients of the pp-wave String Field Theory vertex., 47 pages, 11 figures

In a recent paper, Balthazar, Rodriguez and Yin found remarkable agreement between the one instanton contribution to the scattering amplitudes of two dimensional string theory and those in the matrix model to the first subleading order. The comparison was carried out numerically by analytically continuing the external energies to imaginary values, since for real energies the string theory result diverges. We use insights from string field theory to give finite expressions for the string theory amplitudes for real energies. We also show analytically that the imaginary parts of the string theory amplitudes computed this way reproduce the full matrix model results for general scattering amplitudes involving multiple closed strings., Comment: LaTeX, 14 pages

As briefly explained in the introduction, the BV formalism plays the central role in the construction of a gauge invariant action for string field theory. By now, there are many excellent texts on the BV formalism. We will thus not present a detailed account.

We construct several BV master actions for open superstring field theory in the large Hilbert space. First, we show that a naive use of the conventional BV approach breaks down at the third order of the antifield number expansion, although it enables us to define a simple "string antibracket" taking the Darboux form as space-time antibrackets. This fact implies that in the large Hilbert space, "string fields-antifields" should be reassembled to obtain master actions in a simple manner. We determine the assembly of the string antifields on the basis of Berkovits' constrained BV approach, and give solutions to the master equation defined by Dirac antibrackets on the constrained string field-antifield space. It is expected that partially gauge-fixing enables us to relate superstring field theories based on the large and small Hilbert spaces directly: Reassembling string fields-antifields is rather natural from this point of view. Finally, inspired by these results, we revisit the conventional BV approach and construct a BV master action based on the minimal set of string fields-antifields., Comment: 24 + 4 pages; Published ver

We show how conformal field theory topological defects can relate solutions of open string field theory for different boundary conditions. To this end we generalize the results of Graham and Watts to include the action of defects on boundary condition changing fields. Special care is devoted to the general case when nontrivial multiplicities arise upon defect action. Surprisingly the fusion algebra of defects is realized on open string fields only up to a (star algebra) isomorphism., 67 pages, 23 figures