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In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1 + 1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations not only for small, but even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while in the paramagnetic phase the single magnon excitation governs the dynamics, allowing us to capture the time evolution of the magnetisation using a combination of known results from perturbation theory and form factor based methods. We point out that the dominance of low lying excitations allows for the numerical or experimental determination of the mass spectra through the study of the quench dynamics. [ABSTRACT FROM AUTHOR]

We study numerically three-dimensional Z ( N ) lattice gauge theories at finite temperature, for N = 5 , 6 , 8 , 12 , 13 and 20 on lattices with temporal extension N t = 2 , 4 , 8 . For each model, we locate phase transition points and determine critical indices. We propose also the scaling of critical points with N . The data obtained enable us to verify the scaling near the continuum limit for the Z ( N ) models at finite temperatures. [ABSTRACT FROM AUTHOR]

Abstract: We have measured the correlation function of Polyakov loops on the lattice in three dimensional gauge theory near its finite temperature phase transition. Using a new and powerful application of finite size scaling, we furthermore extend the measurements of the critical couplings to considerably larger values of the lattice sizes, both in the temperature and space directions, than was investigated earlier in this theory. With the help of these measurements we perform a detailed finite size scaling analysis, showing that for the critical exponents of the two dimensional three state Potts model the mass and the susceptibility fall on unique scaling curves. This strongly supports the expectation that the gauge theory is in the same universality class. The Nambu–Goto string model on the other hand predicts that the exponent ν has the mean field value, which is quite different from the value in the abovementioned Potts model. Using our values of the critical couplings we also determine the continuum limit of the value of the critical temperature in terms of the square root of the zero temperature string tension. This value is very near to the prediction of the Nambu–Goto string model in spite of the different critical behaviour. [Copyright &y& Elsevier]

Abstract: Tensor models are a generalization of matrix models (their graphs being dual to higher-dimensional triangulations) and, in their colored version, admit a expansion and a continuum limit. We introduce a new class of colored tensor models with a modified propagator which allows us to associate weight factors to the faces of the graphs, i.e. to the bones (or hinges) of the triangulation, where curvature is concentrated. They correspond to dynamical triangulations in three and higher dimensions with generalized amplitudes. We solve analytically the leading order in of the most general model in arbitrary dimensions. We then show that a particular model, corresponding to dynamical triangulations with a non-trivial measure factor, undergoes a third-order phase transition in the continuum characterized by a jump in the susceptibility exponent. [Copyright &y& Elsevier]

Abstract: A continuum model to study the influence of dislocations on the electronic properties of condensed matter systems is described and analyzed. The model is based on a geometrical formalism that associates a density of dislocations with the torsion tensor and uses the technique of quantum field theory in curved space. When applied to two-dimensional systems with Dirac points like graphene we find that dislocations couple in the form of vector gauge fields similar to these arising from curvature or elastic strain. We also describe the ways to couple dislocations to normal metals with a Fermi surface. [Copyright &y& Elsevier]

Abstract: We study the properties of graphene wormholes in which a short nanotube acts as a bridge between two graphene sheets, where the honeycomb carbon lattice is curved from the presence of 12 heptagonal defects. By taking the nanotube bridge with very small length compared to the radius, we develop an effective theory of Dirac fermions to account for the low-energy electronic properties of the wormholes in the continuum limit, where the frustration induced by the heptagonal defects is mimicked by a line of fictitious gauge flux attached to each of them. We find in particular that, when the effective gauge flux from the topological defects becomes maximal, the zero-energy modes of the Dirac equation can be arranged into two triplets, that can be thought as the counterpart of the two triplets of zero modes that arise in the dual instance of the continuum limit of large spherical fullerenes. We further investigate the graphene wormhole spectra by performing a numerical diagonalization of tight-binding Hamiltonians for very large lattices realizing the wormhole geometry. The correspondence between the number of localized electronic states observed in the numerical approach and the effective gauge flux predicted in the continuum limit shows that graphene wormholes can be consistently described by an effective theory of two Dirac fermion fields in the curved geometry of the wormhole, opening the possibility of using real samples of the carbon material as a playground to experiment with the interaction between the background curvature and the Dirac fields. [Copyright &y& Elsevier]

Abstract: We present a simple lattice formulation of two-dimensional supersymmetric QCD (SQCD) with N matter multiplets in the fundamental representation. The construction uses compact gauge link variables and exactly preserves one linear combination of supercharges on the two-dimensional regular lattice. Artificial saddle points in the weak coupling limit and the species doubling are evaded without imposing the admissibility. A perturbative power-counting argument indicates that the target supersymmetric theory is realized in the continuum limit without any fine tuning. [Copyright &y& Elsevier]

Abstract: The general procedure for obtaining explicit expressions for all cohomologies of Berkovits'' operator is suggested. It is demonstrated that calculation of BV integral for the classical Chern–Simons-like theory (Witten''s OSFT-like theory) reproduces BV version of two-dimensional gauge model at the level of effective action. This model contains gauge field, scalars, fermions and some other fields. We prove that this model is an example of “singular” point from the perspective of the suggested method for cohomology evaluation. For arbitrary “regular” point the same technique results in AKSZ (Alexandrov, Kontsevich, Schwarz, Zaboronsky) version of Chern–Simons theory (BF theory) in accord with [N. Berkovits, Covariant quantization of the superparticle using pure spinors, JHEP 0109 (2001) 016, hep-th/0105050; N. Berkovits, ICTP lectures on covariant quantization of the superstring, hep-th/0209059; M. Movshev, A. Schwarz, On maximally supersymmetric Yang–Mills theories, Nucl. Phys. B 681 (2004) 324, hep-th/0311132; M. Movshev, A. Schwarz, Algebraic structure of Yang–Mills theory, hep-th/0404183]. [Copyright &y& Elsevier]

Abstract: The Jackiw–Pi model in dimensions is a non-relativistic conformal field theory of charged particles with point-like self-interaction. For specific values of the interaction strengths the classical theory possesses vortex and multi-vortex solutions, which are all degenerate in energy. We compute the full set of first-order perturbative quantum corrections. Only the coupling constant requires renormalization; the fields and electric charge e are not renormalized. It is shown that in general the conformal symmetries are broken by an anomalous contribution to the conservation law, proportional to the β-function. However, the β-function vanishes upon restricting the coupling constants to values , which includes the case in which vortex solutions exist. Therefore the existence of vortices also guarantees the preservation of the conformal symmetries. [Copyright &y& Elsevier]

Abstract: We develop Yang–Baxter integrability structures connected with the quantum affine superalgebra . Baxter''s Q-operators are explicitly constructed as super-traces of certain monodromy matrices associated with (q-deformed) bosonic and fermionic oscillator algebras. There are six different Q-operators in this case, obeying a few fundamental fusion relations, which imply all functional relations between various commuting transfer matrices. The results are universal in the sense that they do not depend on the quantum space of states and apply both to lattice models and to continuous quantum field theory models as well. [Copyright &y& Elsevier]

Abstract: A conjecture is presented for the thermal one-point function of boundary operators in integrable boundary quantum field theories in terms of form factors. It is expected to have applications in studying boundary critical phenomena and boundary flows, which are relevant in the context of condensed matter and string theory. The conjectured formula is verified by a low-temperature expansion developed using finite size techniques, which can also be used to evaluate higher point functions both in the bulk and on the boundary. [Copyright &y& Elsevier]

Abstract: We investigate the string field theory around the tachyon vacuum. A pure gauge form of the solution is constructed at the tachyon vacuum. For a special choice of the gauge function for the pure gauge form, marginal deformation from the tachyon vacuum is allowed due to the nontrivial roles of Schnabl''s analytic vacuum solution. We obtain an exact rolling tachyon solution which describes the late time behaviors of D-brane decay. [Copyright &y& Elsevier]

Abstract: The free Schrödinger theory in d space dimensions is a non-relativistic conformal field theory. The interacting non-linear theory preserves this symmetry in specific numbers of dimensions at the classical (tree) level. This holds in particular for the -theory in . We compute the full quantum corrections to the 1PI 4-point function in dimensions and find a non-trivial β-function completely given by the 1-loop result. We exhibit an explicit Ward-identity showing that scale-invariance is broken in the limit by an anomalous contribution proportional to the β-function. [Copyright &y& Elsevier]

Abstract: We calculate gauge invariant observables for Schnabl''s solution with analytic method and with the level truncation approximation. We also compute them for the numerical solution initially obtained by Sen and Zwiebach in the level truncation approximation to compare with the one for Schnabl''s solution. The results are consistent with the expectation that they may be gauge equivalent. We briefly discuss the gauge invariant observables and the action for a marginal solution with a nonsingular current. [Copyright &y& Elsevier]

Abstract: Two-dimensional quantum fields in electric and gravitational backgrounds can be described by conformal field theories, and hence all the physical (covariant) quantities can be written in terms of the corresponding holomorphic quantities. In this paper, we first derive relations between covariant and holomorphic forms of higher-spin currents in these backgrounds, and then, by using these relations, obtain higher-spin generalizations of the trace and gauge (or gravitational) anomalies up to spin 4. These results are applied to derive higher-moments of Hawking fluxes in black holes in a separate paper [S. Iso, T. Morita, H. Umetsu, Hawking radiation via higher-spin gauge anomalies, arXiv: 0710.0456 [hep-th]]. [Copyright &y& Elsevier]

Abstract: The boundary entropy of a critical one-dimensional quantum system (or two-dimensional conformal field theory) is known to decrease under renormalization group (RG) flow of the boundary theory. We study instead the behavior of the boundary entropy as the bulk theory flows between two nearby critical points. We use conformal perturbation theory to calculate the change in g due to a slightly relevant bulk perturbation and find that it has no preferred sign. The boundary entropy can therefore increase during appropriate bulk flows. This is demonstrated explicitly in flows between minimal models. We discuss the applications of this result to D-branes in string theory and to impurity problems in condensed matter. [Copyright &y& Elsevier]

Abstract: The physical properties of arbitrary half-integer spins fermionic cold atoms loaded into a one-dimensional optical lattice are investigated by means of a conformal field theory approach. We show that for attractive interactions two different superfluid phases emerge for : A BCS pairing phase, and a molecular superfluid phase which is formed from bound-states made of 2N fermions. In the low-energy approach, the competition between these instabilities and charge-density waves is described in terms of parafermionic degrees of freedom. The quantum phase transition for is universal and shown to belong to the Ising and three-state Potts universality classes respectively. In contrast, for , the transition is non-universal. For a filling of one atom per site, a Mott transition occurs and the nature of the possible Mott-insulating phases are determined. [Copyright &y& Elsevier]

Abstract: We construct the four-point correlation functions containing the top component of the supermultiplet in the Neveu–Schwarz sector of the SUSY Liouville field theory. The construction is based on the recursive representation for the NS conformal blocks. We test our results in the case where one of the fields is degenerate with a singular vector on the level 3/2. In this case, the correlation function satisfies a third-order ordinary differential equation, which we derive. We numerically verify the crossing symmetry relations for the constructed correlation functions in the nondegenerate case. [Copyright &y& Elsevier]

Abstract: A supersymmetric Hamiltonian is constructed for the edge excitations of the Moore–Read (Pfaffian) like state, which is a realization of the supersymmetric CS model. Fermionic generators and their conjugates are introduced to deal with the fermion pairing, whose condensation form a BCS like state. After Bogoliubov transformation, an supersymmetric and nonrelativistic Hamiltonian is found to take a known form, which is integrable. The main difference between the Moore–Read state and our BCS like state is that the number of fermion pairs in our formalism is not fixed. However, we have also found that the excited states in our model looks similar but not exactly the same as Moore and Read''s. [Copyright &y& Elsevier]

Abstract: We present the two-loop virtual QCD corrections to the production of heavy quarks in gluon fusion. The results are exact in the limit when all kinematical invariants are large compared to the mass of the heavy quark up to terms suppressed by powers of the heavy-quark mass. Our derivation uses a simple relation between massless and massive QCD scattering amplitudes as well as a direct calculation of the massive amplitude at two loops. The results presented here together with those obtained previously for quark–quark scattering form important parts of the next-to-next-to-leading order QCD corrections to heavy-quark production in hadron–hadron collisions. [Copyright &y& Elsevier]

Abstract: We calculate bosonic massive closed string states at arbitrary mass levels scattered from orientifold planes in the high-energy, fixed angle limit. For the case of O-particle scatterings, we obtain infinite linear relations among high-energy scattering amplitudes of different string states. We also confirm that there exist only closed string Regge poles in the form factor of the O-particle amplitudes as expected. For the case of O-domain-wall scatterings, we find that, like the well-known D-instanton scatterings, the amplitudes behave like field theory scatterings, namely UV power-law without infinite Regge poles. In addition, we discover that there exist only finite number of t-channel closed string poles in the form factor of O-domain-wall scatterings, and the masses of the poles are bounded by the masses of the external legs. We thus confirm that all massive closed string states do couple to the O-domain-wall. [Copyright &y& Elsevier]

Abstract: The tree-level amplitudes in the β-deformed supersymmetric gauge theory are derived from twistor string theory. We first show that a simple generalization of [M. Kulaxizi, K. Zoubos, Marginal deformations of SYM from open/closed twistor strings, Nucl. Phys. B 738 (2006) 317, hep-th/0410122] gives us the desired results for all the tree-level amplitudes up to first order in the deformation parameter β. Then we provide a new proposal which matches field theory to all orders of β. With our deformed twistor string theory, it can be shown that integration over connected instantons and disconnected instantons remain equivalent. The tree-level amplitudes in the non-supersymmetric γ-deformed theory can be obtained using a similar deformation of the twistor string. Finally, we find improved twistor string results for the tree-level purely gluonic amplitudes in theories with more general marginal deformations. [Copyright &y& Elsevier]

Abstract: We consider classical superstring theories on flat four-dimensional space–times, and where or supersymmetry is spontaneously broken. We obtain the thermal and quantum corrections at the string one-loop level and show that the back-reaction on the space–time metric induces a cosmological evolution. We concentrate on heterotic string models obtained by compactification on a torus and on orbifolds. The temperature T and the supersymmetry breaking scale M are generated via the Scherk–Schwarz mechanism on the Euclidean time cycle and on an internal spatial cycle respectively. The effective field theory corresponds to a no-scale supergravity, where the corresponding no-scale modulus controls the SUSY-breaking scale. The classical flatness of this modulus is lifted by an effective thermal potential, given by the free energy. The gravitational field equations admit solutions where M, T and the inverse scale factor of the universe remain proportional. In particular the ratio is fixed during time evolution. The induced cosmology is governed by a Friedmann–Hubble equation involving an effective radiation term and an effective curvature term , whose coefficients are functions of the complex structure ratio . [Copyright &y& Elsevier]

Abstract: We propose a simple effective model for the description of interfaces in 2d statistical models, based on the first-order treatment of an action corresponding to the length of the interface. The universal prediction of this model for the interface free energy agrees with the result of an exact calculation in the case of the 2d Ising model. This model appears as a dimensional reduction of the Nambu–Goto stringy description of interfaces in 3d, i.e., of the capillary wave model. [Copyright &y& Elsevier]

Abstract: The ground state and low energy excitations of the supersymmetric Haldane–Shastry spin chain are analyzed. In the thermodynamic limit, it is found that the ground state degeneracy is finite only for the and spin chains, while the dispersion relation for the low energy and low momentum excitations is linear for all values of m and n. We show that the low energy excitations of the spin chain are described by a conformal field theory of m non-interacting Dirac fermions which have only positive energies; the central charge of this theory is . Finally, for , the partition functions of the Haldane–Shastry spin chain and the Polychronakos spin chain are shown to be related in a simple way in the thermodynamic limit at low temperatures. [Copyright &y& Elsevier]

Abstract: We derive non-perturbative sum rules in lattice gauge theory at finite temperature. They relate the susceptibilities of the trace anomaly and energy–momentum tensor to temperature derivatives of the thermodynamic potentials. Two of them have been derived previously in the continuum and one is new. In all cases, at finite lattice spacing there are important corrections to the continuum sum rules that are only suppressed by the bare coupling . We also show how the discretization errors affecting the thermodynamic potentials can be controlled by computing these susceptibilities. [Copyright &y& Elsevier]

Abstract: We investigate some aspects of the relationship between matrix string theory and light-cone string field theory by analysing the correspondence between the two-loop thermal partition function of DLCQ strings in flat space and the integrated two-point correlator of twist fields in a symmetric product orbifold conformal field theory at one-loop order. This is carried out by deriving combinatorial expressions for generic twist field correlation functions in permutation orbifolds using the covering surface method, by deriving the one-loop modification of the twist field interaction vertex, and by relating the two-loop finite temperature DLCQ string theory to the theory of Prym varieties for genus two covers of an elliptic curve. The case of bosonic orbifolds is worked out explicitly and precise agreement between both amplitudes is found. We use these techniques to derive explicit expressions for orbifold spin twist field correlation functions in the type II and heterotic string theories. [Copyright &y& Elsevier]

Abstract: We consider the de Sitter cosmology deformed by the presence of a thermal bath of radiation and/or time-dependent moduli fields. Depending on the parameters, either a first or second-order phase transition can occur. In the first case, an instanton allows a double analytic continuation. It induces a probability to enter the inflationary evolution by tunnel effect from another cosmological solution. The latter starts with a big bang and, in the case the transition does not occur, ends with a big crunch. A temperature duality exchanges the two cosmological branches. In the limit where the pure de Sitter universe is recovered, the tunnel effect reduces to a “creation from nothing”, due to the vanishing of the big bang branch. However, the latter may be viable in some range of the deformation parameter. In the second case, there is a smooth evolution from a big bang to the inflationary phase. [Copyright &y& Elsevier]

Abstract: We extend our earlier work, regarding the perturbative stability of string configurations used for computing the interaction potential of heavy quarks within the gauge/gravity correspondence, to cover a more general class of gravity duals. We provide results, mostly based on analytic methods and corroborated by numerical calculations, which apply to strings in a general class of backgrounds that encompass boosted, spinning and marginally-deformed D3-brane backgrounds. For the case of spinning branes we demonstrate in a few examples that perturbative stability of strings may require strong conditions complementing those following by thermodynamic stability of the dual field theories. For marginally-deformed backgrounds, we find that even in the conformal case stability requires an upper value for the imaginary part σ of the deformation parameter, whereas in regions of the Coulomb branch where there exists linear confinement we find that there exist stable string configurations for certain ranges of values of the parameter σ. We finally discuss the case of open strings with fixed endpoints propagating in Rindler space, which turns out to have an exact classical-mechanical analog. [Copyright &y& Elsevier]

Abstract: We perform a dedicated study of the four-fermion production process near the W pair-production threshold in view of the importance of this process for a precise measurement of the W boson mass. Accurate theoretical predictions for this process require a systematic treatment of finite-width effects. We use unstable-particle effective field theory (EFT) to perform an expansion in the coupling constants, , and the non-relativistic velocity v of the W boson up to next-to-leading order in . We find that the dominant theoretical uncertainty in is currently due to an incomplete treatment of initial-state radiation. The remaining uncertainty of the NLO EFT calculation translates into , and to about 5 MeV with additional input from the NLO four-fermion calculation in the full theory. [Copyright &y& Elsevier]

Abstract: The choice of a star product realization for non-commutative field theory can be regarded as a gauge choice in the space of all equivalent star products. With the goal of having a gauge invariant treatment, we develop tools, such as integration measures and covariant derivatives on this space. The covariant derivative can be expressed in terms of connections in the usual way giving rise to new degrees of freedom for non-commutative theories. [Copyright &y& Elsevier]

Abstract: The q-state Potts field theory describes the universality class associated to the spontaneous breaking of the permutation symmetry of q colors. In two dimensions it is defined up to and exhibits duality and integrability away from critical temperature in absence of magnetic field. We show how, when a magnetic field is switched on, it provides the simplest model of confinement allowing for both mesons and baryons. Deconfined quarks (kinks) exist in a phase bounded by a first order transition on one side, and a second order transition on the other. The evolution of the mass spectrum with temperature and magnetic field is discussed. [Copyright &y& Elsevier]

Abstract: The free field partition function for a generic gauge theory, where the fundamental fields transform in the adjoint representation, is analysed in terms of symmetric polynomial techniques. It is shown by these means how this is related to the cycle polynomial for the symmetric group and how the large N result may be easily recovered. Higher order corrections for finite N are also discussed in terms of symmetric group characters. For finite N, the partition function involving a single bosonic fundamental field is recovered and explicit counting of multi-trace quarter BPS operators in free super-Yang–Mills discussed, including a general result for large N. The partition function for quarter BPS operators in the chiral ring of super-Yang–Mills is analysed in terms of plane partitions. Asymptotic counting of BPS primary operators with differing R-symmetry charges is discussed in both free super-Yang–Mills and in the chiral ring. Also, general and explicit expressions are derived for gauge theory partition functions, when the fundamental fields transform in the adjoint, for free field theory. [Copyright &y& Elsevier]

Abstract: We review the topological quantum computation scheme of Das Sarma et al. from the perspective of the conformal field theory for the two-dimensional critical Ising model. This scheme originally used the monodromy properties of the non-Abelian excitations in the Pfaffian quantum Hall state to construct elementary qubits and execute logical NOT on them. We extend the scheme of Das Sarma et al. by exploiting the explicit braiding transformations for the Pfaffian wave functions containing 4 and 6 quasiholes to implement, for the first time in this context, the single-qubit Hadamard and phase gates and the two-qubit Controlled-NOT gate over Pfaffian qubits in a topologically protected way. In more detail, we explicitly construct the unitary representations of the braid groups , and and use the elementary braid matrices to implement one-, two- and three-qubit gates. We also propose to construct a topologically protected Toffoli gate, in terms of a braid-group based Controlled–Controlled-Z gate precursor. Finally we discuss some difficulties arising in the embedding of the Clifford gates and address several important questions about topological quantum computation in general. [Copyright &y& Elsevier]

Abstract: We study the extraction of Δ-resonance parameters from lattice data for small quark masses, corresponding to the case of an unstable Δ. To this end, we calculate the spectrum of the correlator of two Δ-fields in a finite Euclidean box up-to-and-including in the small scale expansion using infrared regularization. On the basis of our numerical study, we argue that the extraction of the parameters of the Δ-resonance (in particular, of the mass and the pion–nucleon–delta coupling constant) from the measured volume dependence of the lowest energy levels should be feasible. [Copyright &y& Elsevier]

Abstract: We propose a Hodge field theory construction that captures algebraic properties of the reduction of Zwiebach invariants to Gromov–Witten invariants. It generalizes the Barannikov–Kontsevich construction to the case of higher genera correlators with gravitational descendants. We prove the main theorem stating that algebraically defined Hodge field theory correlators satisfy all tautological relations. From this perspective the statement that Barannikov–Kontsevich construction provides a solution of the WDVV equation looks as the simplest particular case of our theorem. Also it generalizes the particular cases of other low-genera tautological relations proven in our earlier works; we replace the old technical proofs by a novel conceptual proof. [Copyright &y& Elsevier]

Abstract: We establish a correspondence between the resummation of world lines and the diagonalization of the Hamiltonian for a strongly correlated electronic system. For this purpose, we analyze the functional integrals for the partition function and the correlation functions invoking a slave boson representation in the radial gauge. We show in the spinless case that the Green''s function of the physical electron and the projected Green''s function of the pseudofermion coincide. Correlation and Green''s functions in the spinful case involve a complex entanglement of the world lines which, however, can be obtained through a strikingly simple extension of the spinless scheme. As a toy model we investigate the two-site cluster of the single impurity Anderson model which yields analytical results. All expectation values and dynamical correlation functions are obtained from the exact calculation of the relevant functional integrals. The hole density, the hole auto-correlation function and the Green''s function are computed, and a comparison between spinless and spin 1/2 systems provides insight into the role of the radial slave boson field. In particular, the exact expectation value of the radial slave boson field is finite in both cases, and it is not related to a Bose condensate. [Copyright &y& Elsevier]

Abstract: Using the recently introduced boundary form factor bootstrap equations, we map the complete space of their solutions for the boundary version of the scaling Lee–Yang model and sinh-Gordon theory. We show that the complete space of solutions, graded by the ultraviolet behaviour of the form factors can be brought into correspondence with the spectrum of local boundary operators expected from boundary conformal field theory, which is a major evidence for the correctness of the boundary form factor bootstrap framework. [Copyright &y& Elsevier]

Abstract: We discuss D3-branes on cohomogeneity-three resolved Calabi–Yau cones over spaces, for which a 2-cycle or 4-cycle has been blown up. In terms of the dual quiver gauge theory, this corresponds to motion along the non-mesonic, or baryonic, directions in the moduli space of vacua. In particular, a dimension-two and/or dimension-six scalar operator gets a vacuum expectation value. These resolved cones support various harmonic -forms which reduce the ranks of some of the gauge groups either by a Seiberg duality cascade or by Higgsing. We also discuss higher-dimensional resolved Calabi–Yau cones. In particular, we obtain square-integrable -forms for eight-dimensional cohomogeneity-four Calabi–Yau metrics. [Copyright &y& Elsevier]

Abstract: As a step towards formulating projective superspace techniques for supergravity theories with eight supercharges, this work is devoted to field theory in five-dimensional anti-de Sitter superspace which is a maximally symmetric curved background. We develop the differential geometry of and describe its isometries in terms of Killing supervectors. Various off-shell supermultiplets in are defined, and supersymmetric actions are constructed both in harmonic and projective superspace approaches. Several families of supersymmetric theories are presented including nonlinear sigma-models, Chern–Simons theories and vector–tensor dynamical systems. Using a suitable coset representative, we make use of the coset construction to develop an explicit realization for one half of the superspace as a trivial fiber bundle with fibers isomorphic to four-dimensional Minkowski superspace. [Copyright &y& Elsevier]

Abstract: We study the zero-temperature partition function of the Potts antiferromagnet (i.e., the chromatic polynomial) on a torus using a transfer-matrix approach. We consider square- and triangular-lattice strips with fixed width L, arbitrary length N, and fully periodic boundary conditions. On the mathematical side, we obtain exact expressions for the chromatic polynomial of widths , 6, 7 for the square and triangular lattices. On the physical side, we obtain the exact phase diagrams for these strips of width L and infinite length, and from these results we extract useful information about the infinite-volume phase diagram of this model: in particular, the number and position of the different phases. [Copyright &y& Elsevier]

Abstract: We consider discretized gravity in six dimensions, where the two extra dimensions have been compactified on a hyperbolic disk of constant curvature. We analyze different realizations of lattice gravity on the disk at the level of an effective field theory for massive gravitons. It is shown that the observed strong coupling scale of lattice gravity in discretized five-dimensional flat or warped space can be increased if the latticized fifth dimension is wrapped around a hyperbolic disk that has a non-trivial warp factor. As an application, we also study the generation of naturally small Dirac neutrino masses via a discrete volume suppression mechanism and discuss briefly collider implications of our model. [Copyright &y& Elsevier]

Abstract: Putting a twisted version of super-Yang–Mills on a curved four-dimensional manifold generically breaks all conformal supersymmetries. In the special case where the four-manifold is a cone, we show that exactly two conformal supercharges remain unbroken. We construct an off-shell formulation of the theory such that the two unbroken conformal supercharges combine into a family of topological charges parameterized by . The resulting theory is topological in the sense that it is independent of the metric on the three-dimensional base of the cone. [Copyright &y& Elsevier]

Abstract: The minimal models with have a unique (non-trivial) simple current of conformal dimension . The representation theory of the extended algebra defined by this simple current is investigated in detail. All highest weight representations are proved to be irreducible: There are thus no singular vectors in the extended theory. This has interesting structural consequences. In particular, it leads to a recursive method for computing the various terms appearing in the operator product expansion of the simple current with itself. The simplest extended models are analysed in detail and the question of equivalence of conformal field theories is carefully examined. [Copyright &y& Elsevier]

Abstract: A new powerful method to test the stability of the replica symmetric spin glass phase is proposed by introducing a replicon generator function . Exact symmetry arguments are used to prove that its extremum is proportional to the inverse spin glass susceptibility. By the idea of independent droplet excitations a scaling form for can be derived, whereas it can be exactly computed in the mean field Sherrington–Kirkpatrick model. It is shown by a first order perturbative treatment that the replica symmetric phase is unstable down to dimensions , and the mean field scaling function proves to be very robust. Although replica symmetry breaking is escalating for decreasing dimensionality, a mechanism caused by the infrared divergent replicon propagator may destroy the mean field picture at some low enough dimension. [Copyright &y& Elsevier]

Abstract: We consider quantum field theories with boundary on a codimension one hyperplane. Using dimensional examples, we clarify the relation between three parameters characterizing one-point functions, finite size corrections to the ground state energy and the singularity structure of scattering amplitudes, respectively. We then develop the formalism of boundary states in general spacetime dimensions and relate the cluster expansion of the boundary state to the correlation functions using reduction formulae. This allows us to derive the cluster expansion in terms of the boundary scattering amplitudes, and to give a derivation of the conjectured relations between the parameters in dimensions, and their generalization to dimensions. We use these results to express the large volume asymptotics of the Casimir effect in terms of the one-point functions or alternatively the singularity structure of the one-particle reflection factor, and for the case of vanishing one-particle couplings we give a complete proof of our previous result for the leading behaviour. [Copyright &y& Elsevier]

Abstract: The correspondence between ordinary differential equations and Bethe ansatz equations for integrable lattice models in their continuum limits is generalised to vertex models related to classical simple Lie algebras. New families of pseudo-differential equations are proposed, and a link between specific generalised eigenvalue problems for these equations and the Bethe ansatz is deduced. The pseudo-differential operators resemble in form the Miura-transformed Lax operators studied in work on generalised KdV equations, classical W-algebras and, more recently, in the context of the geometric Langlands correspondence. Negative-dimension and boundary-condition dualities are also observed. [Copyright &y& Elsevier]

Abstract: We study the relationship between instanton counting in Yang–Mills theory on a generic four-dimensional toric orbifold and the semi-classical expansion of q-deformed Yang–Mills theory on the blowups of the minimal resolution of the orbifold singularity, with an eye to clarifying the recent proposal of using two-dimensional gauge theories to count microstates of black holes in four dimensions. We describe explicitly the instanton contributions to the counting of D-brane bound states which are captured by the two-dimensional gauge theory. We derive an intimate relationship between the two-dimensional Yang–Mills theory and Chern–Simons theory on generic Lens spaces, and use it to show that the known instanton counting is only reproduced when the Chern–Simons contributions are treated as non-dynamical boundary conditions in the D4-brane gauge theory. We also use this correspondence to discuss the counting of instantons on higher genus ruled Riemann surfaces. [Copyright &y& Elsevier]

Abstract: We solve a new chiral random two-matrix theory by means of biorthogonal polynomials for any matrix size N. By deriving the relevant kernels we find explicit formulas for all -point spectral (mixed or unmixed) correlation functions. In the microscopic limit we find the corresponding scaling functions, and thus derive all spectral correlators in this limit as well. We extend these results to the ordinary (non-chiral) ensembles, and also there provide explicit solutions for any finite size N, and in the microscopic scaling limit. Our results give the general analytical expressions for the microscopic correlation functions of the Dirac operator eigenvalues in theories with imaginary baryon and isospin chemical potential, and can be used to extract the tree-level pion decay constant from lattice gauge theory configurations. We find exact agreement with previous computations based on the low-energy effective field theory in the two special cases where comparisons are possible. [Copyright &y& Elsevier]

Abstract: In this work we develop the BRST approach to Lagrangian construction for the massive integer higher spin fields in an arbitrary dimensional AdS space. The theory is formulated in terms of auxiliary Fock space. Closed nonlinear symmetry algebra of higher spin bosonic theory in AdS space is found and a method of deriving the BRST operator for such an algebra is proposed. A general procedure of Lagrangian construction, describing the dynamics of a bosonic field with any spin is given on the base of the BRST operator. No off-shell constraints on the fields and the gauge parameters are used from the very beginning. As an example of general procedure, we derive the Lagrangians for massive bosonic fields with spin 0, 1 and 2, containing the total set of auxiliary fields and gauge symmetries. [Copyright &y& Elsevier]