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We study classical closed bosonic strings probing the near-horizon region of a non-extremal black hole and show that this corresponds to understanding string theory in the Carroll regime. This is done by first performing a Carroll expansion and then a near-horizon expansion of a closed relativistic string, subsequently showing that they agree. Concretely, we expand the phase space action in powers of c2, where c is the speed of light, assuming that the target space admits a string Carroll expansion (where two directions are singled out) and show that there exist two different Carroll strings: a magnetic and an electric string. The magnetic string has a Lorentzian worldsheet, whereas the worldsheet of the electric string is Carrollian. The geometry near the horizon of a four-dimensional (4D) Schwarzschild black hole takes the form of a string Carroll expansion (a 2D Rindler space fibred over a 2-sphere). We show that the solution space of relativistic strings near the horizon bifurcates and the two sectors precisely match with the magnetic/electric Carroll strings with an appropriate target space. Magnetic Carroll strings near a black hole shrink to a point on the two-sphere and either follow null geodesics or turn into folded strings on the 2D Rindler spacetime. Electric Carroll strings wrap the two-sphere and follow a massive geodesic in the Rindler space. Finally, we show that 4D non-extremal Kerr and Reissner-Nordström black holes also admit string Carroll expansions near their outer horizons, indicating that our formulation extends to generic non-extremal black holes. [ABSTRACT FROM AUTHOR]

With the goal of building a concrete co-dimension one holographically dual field theory for four dimensional asymptotically flat spacetimes (4d AFS) as a limit of AdS4/CFT3, we begin an investigation of 3d Chern-Simons matter (CSM) theories in the Carroll regime. We perform a Carroll (speed of light c → 0) expansion of the relativistic Chern-Simons action coupled to a massless scalar and obtain Carrollian CSM theories, which we show are invariant under the infinite dimensional 3d conformal Carroll or 4d Bondi-van der Burg-Metzner-Sachs (BMS4) symmetries, thus making them putative duals for 4d AFS. Concentrating on the leading-order electric Carroll CSM theory, we perform a null reduction of the 3d theory. Null reduction is a procedure to obtain non-relativistic theories from a higher dimensional relativistic theory. Curiously, null reduction of a Carrollian theory yields a relativistic lower-dimensional theory. We work with SU(N) × SU(M) CS theory coupled to bi-fundamental matter and show that when N = M, we obtain (rather surprisingly) a 2d Euclidean Yang-Mills theory after null reduction. We also comment on the reduction when N ≠ M and possible connections of the null-reduced Carroll theory to a candidate 2d Celestial CFT. [ABSTRACT FROM AUTHOR]

We introduce null contractions of the Poincare and relativistic conformal algebras. The longitudinal null contraction involves writing the algebra in lightcone coordinates and contracting one of the null directions. For the Poincare algebra, this yields two non-overlapping co-dimension one Carroll algebras. The transverse contraction is a limit on the spatial dimensions and yields two non-overlapping co-dimension one Galilean algebras. We find, similar to Susskind's original observation of the non-relativistic case, that the Poincare algebra, written in the lightcone coordinates, naturally contains Carrollian sub-algebras in one lower dimension. The effect of the longitudinal contraction, which essentially focusses on the null direction, is to disentangle the two Carroll algebras that now correspond to the symmetries of the two null boundaries. The transverse contraction similarly separates the overlapping Galilean sub-algebras of the original Poincare algebra. We discuss aspects of the conformal case, where we get lower dimensional Carroll Conformal algebras and Schrödinger algebras. [ABSTRACT FROM AUTHOR]

We compare and contrast the two approaches of holography in asymptotically flat spacetimes, viz. the co-dimension two Celestial approach based on the Mellin transformation and the co-dimension one Carrollian approach based on the modified Mellin and elucidate how some of the problems of the Celestial approach can be rectified by the Carrollian one. Considering flat holography as a limit from AdS/CFT makes a co-dimension one dual more plausible, and our previous construction of Carrollian correlations from AdS Witten diagrams is testimony to this. In this paper, we show how to generalize our earlier analysis for operators with spin. We work out a large number of explicit non-trivial examples (twelve) and show matching between the limit of AdS4 Witten diagrams and 3d boundary symmetry considerations, thus making the case for the Carrollian dual even stronger. [ABSTRACT FROM AUTHOR]

At extreme energies, both low and high, the spacetime symmetries of relativistic quantum field theories (QFTs) are expected to change with Galilean symmetries emerging in the very low energy domain and, as we will argue, Carrollian symmetries appearing at very high energies. The formulation of Wilsonian renormalisation group seems inadequate for handling these changes of the underlying Poincare symmetry of QFTs and it seems unlikely that these drastic changes can be seen within the realms of relativistic QFT. We show that contrary to this expectation, changes in the spacetime algebra occurs at the very edges of parameter space. In particular, we focus on the very high energy sector and show how bilinears of U(1) currents added to a two dimensional (massless) scalar field theory deform the relativistic spacetime conformal algebra to conformal Carroll as the effective coupling of the deformation is dialed to infinity. We demonstrate this using both a symmetric and an antisymmetric current-current deformation for theories with multiple scalar fields. These two operators generate distinct kinds of quantum flows in the coupling space, the symmetric driven by Bogoliubov transformations and the antisymmetric by spectral flows, both leading to Carrollian CFTs at the end of the flow. [ABSTRACT FROM AUTHOR]

Flat space cosmologies (FSCs) are time dependent solutions of three-dimensional (3D) gravity with a vanishing cosmological constant. They can be constructed from a discrete quotient of empty 3D flat spacetime and are also called shifted-boost orbifolds. Using this quotient structure, we build a new and generalized Selberg zeta function for FSCs, and show that it is directly related to the scalar 1-loop partition function. We then propose an extension of this formalism applicable to more general quotient manifolds M /ℤ, based on representation theory of fields propagating on this background. Our prescription constitutes a novel and expedient method for calculating regularized 1-loop determinants, without resorting to the heat kernel. We compute quasinormal modes in the FSC using the zeroes of a Selberg zeta function, and match them to known results. [ABSTRACT FROM AUTHOR]

Two-dimensional (2d) field theories invariant under the Bondi-Metzner-Sachs algebra, or 2d BMSFTs in short, are putative holographic duals of Einstein gravity in 3d asymptotically flat spacetimes. When defined on a torus, these field theories come equipped with a modified modular structure. We use the modular covariance of the BMS torus two-point function to develop formulae for different three-point structure constants of the field theory. These structure constants indicate that BMSFTs follow the eigenstate thermalization hypothesis, albeit with some interesting changes to usual 2d CFTs. The singularity structures of the structure constants contain information on perturbations of cosmological horizons in 3d asymptotically flat spacetimes, which we show can also be obtained as a limit of BTZ quasinormal modes. [ABSTRACT FROM AUTHOR]

Carrollian Conformal Field Theories (CFTs) have been proposed as co-dimension one holographic duals to asymptotically flat spacetimes as opposed to Celestial CFTs which are co-dimension two. In this paper, drawing inspiration from Celestial holography, we show by a suitable generalisation of the flat space limit of AdS that keeps track of the previously disregarded null direction, one can reproduce Carrollian CFT correlation functions from AdS Witten diagrams. In particular, considering Witten diagrams in AdS4, we reproduce two and three-point correlation functions for three dimensional Carrollian CFTs in the so-called delta-function branch. Along the way, we construct non-trivial Carrollian three-point functions in the delta-branch by considering a collinear limit. We also obtain a generalised anti-podal matching condition that now depends on the retarded time direction. [ABSTRACT FROM AUTHOR]

The Carroll algebra is constructed as the c → 0 limit of the Poincare algebra and is associated to symmetries on generic null surfaces. In this paper, we begin investigations of Carrollian fermions or fermions defined on generic null surfaces. Due to the availability of two different (degenerate) metrics on Carroll spacetimes, there is the possibility of two different versions of Carroll Clifford algebras. We consider both possibilities and construct explicit representations of Carrollian gamma matrices and show how to build higher spacetime dimensional representations out of lower ones. Actions for Carroll fermions are constructed with these gamma matrices and the properties of these actions are investigated. We show that in condensed matter systems where the dispersion relation becomes trivial i.e. the energy is not dependent on momentum and bands flatten out, Carroll symmetry generically appears. We give explicit examples of this including that of twisted bi-layer graphene, where superconductivity appears at so called magic angles and connect this to Carroll fermions. [ABSTRACT FROM AUTHOR]

We investigate two dimensional (2d) quantum field theories which exhibit Non-Lorentzian Kač-Moody (NLKM) algebras as their underlying symmetry. Our investigations encompass both 2d Galilean (speed of light c → ∞) and Carrollian (c → 0) CFTs with additional number of infinite non-Abelian currents, stemming from an isomorphism between the two algebras. We alternate between an intrinsic and a limiting analysis. Our NLKM algebra is constructed first through a contraction and then derived from an intrinsically Carrollian perspective. We then go on to use the symmetries to derive a Non-Lorentzian (NL) Sugawara construction and ultimately write down the NL equivalent of the Knizhnik Zamolodchikov equations. All of these are also derived from contractions, thus providing a robust cross-check of our analyses. [ABSTRACT FROM AUTHOR]

Conformal Carroll symmetry generically arises on null manifolds and is important for holography of asymptotically flat spacetimes, generic black hole horizons and tensionless strings. In this paper, we focus on two dimensional (2d) null manifolds and hence on the 2d Conformal Carroll or equivalently the 3d Bondi-Metzner-Sachs (BMS) algebra. Using Carroll covariance, we write the most general free massless Carroll scalar field theory and discover three inequivalent actions. Of these, two viz. the time-like and space-like actions, have made their appearance in literature before. We uncover a third that we call the mixed-derivative theory. As expected, all three theories enjoy off-shell BMS invariance. Interestingly, we find that the on-shell symmetry of mixed derivative theory is a single Virasoro algebra instead of the full BMS. We discuss potential applications to tensionless strings and flat holography. [ABSTRACT FROM AUTHOR]

Bondi-Metzner-Sachs (BMS) symmetries, or equivalently Conformal Carroll symmetries, are intrinsically associated to null manifolds and in two dimensions can be obtained as an Inönü-Wigner contraction of the two-dimensional (2d) relativistic conformal algebra. Instead of performing contractions, we demonstrate in this paper how this transmutation of symmetries can be achieved by infinite boosts or degenerate linear transformations on coordinates. Taking explicit cues from the worldsheet theory of null strings, we show boosting the system is equivalent to adding a current-current deformation term to the Hamiltonian. As the strength of this deformation term reaches a critical value, the classical symmetry algebra "flows" from two copies of Virasoro to the BMS algebra. We further explore the situation where the CFT coordinates are asymmetrically transformed, and degenerate limits lead to chiral theories. [ABSTRACT FROM AUTHOR]

We investigate the supersymmetric versions of Bondi-Metzner-Sachs or, equivalently, conformal Carroll symmetry in boundary dimensions d > 3, with applications of flat space holography in mind. We identify the contraction of the relativistic symmetry relevant for our purposes and construct a finite-dimensional Carrollian superconformal algebra (CSA) before proposing an infinite-dimensional lift. We provide the superspace formulation for N = 1 CSA and work towards an understanding of the representation theory of the algebra. We conclude with some aspects of N > 1 CSA. [ABSTRACT FROM AUTHOR]

The tensionless limit of string theory has recently been formulated in terms of worldsheet Rindler physics. In this paper, by considering closed strings moving in background Rindler spacetimes, we provide a concrete exemplification of this phenomenon. We first show that strings probing the near-horizon region of a generic non-extremal blackhole become tensionless thereby linking a spacetime Carroll limit to a worldsheet Carroll limit. Then, considering strings in d-dimensional Rindler spacetime we find a Rindler structure induced on the worldsheet. Novelties, including folds, appear on the closed string worldsheet pertaining to the formation of the worldsheet horizon. The closed string becomes segmented at these folding points and different segments go into the formation of closed strings in the different Rindler wedges. The Bondi-Metzner-Sachs (BMS) or the Conformal Carroll algebra emerges from the closed string Virasoro algebra as the horizon is hit. Quantum states on these accelerated worldsheets are discussed and we show the formation of boundary states from gluing conditions of the different segments of the accelerated closed string. [ABSTRACT FROM AUTHOR]

Recently, a careful canonical quantisation of the theory of closed bosonic tensionless strings has resulted in the discovery of three separate vacua and hence three different quantum theories that emerge from this single classical tensionless theory. In this note, we perform lightcone quantisation with the aim of determination of the critical dimension of these three inequivalent quantum theories. The satisfying conclusion of a rather long and tedious calculation is that one of vacua does not lead to any constraint on the number of dimensions, while the other two give D = 26. This implies that all three quantum tensionless theories can be thought of as consistent sub-sectors of quantum tensile bosonic closed string theory. [ABSTRACT FROM AUTHOR]

Two dimensional field theories with Bondi-Metzner-Sachs symmetry have been proposed as duals to asymptotically flat spacetimes in three dimensions. These field theories are naturally defined on null surfaces and hence are conformal cousins of Carrollian theories, where the speed of light goes to zero. In this paper, we initiate an investigation of anomalies in these field theories. Specifically, we focus on the BMS equivalent of Weyl invariance and its breakdown in these field theories and derive an expression for Weyl anomaly. Considering the transformation of partition functions under this symmetry, we derive a Carrollian Liouville action different from ones obtained in the literature earlier. [ABSTRACT FROM AUTHOR]

Two dimensional field theories invariant under the Bondi-Metzner-Sachs (BMS) group are conjectured to be dual to asymptotically flat spacetimes in three dimensions. In this paper, we continue our investigations of the modular properties of these field theories. In particular, we focus on the BMS torus one-point function. We use two different methods to arrive at expressions for asymptotic structure constants for general states in the theory utilising modular properties of the torus one-point function. We then concentrate on the BMS highest weight representation, and derive a host of new results, the most important of which is the BMS torus block. In a particular limit of large weights, we derive the leading and sub-leading pieces of the BMS torus block, which we then use to rederive an expression for the asymptotic structure constants for BMS primaries. Finally, we perform a bulk computation of a probe scalar in the background of a flatspace cosmological solution based on the geodesic approximation to reproduce our field theoretic results. [ABSTRACT FROM AUTHOR]

Within the premise of canonical quantisation, we re-examine the quantum structure of bosonic tensionless string theory. In the classical theory, the worldsheet metric degenerates and the Bondi-Metnzer-Sachs (BMS) algebra arises as the residual symmetries on fixing the tensionless equivalent of the conformal gauge. In the quantum regime, we find, on careful examination, that there are multiple ways to impose constraints to restrict the physical Hilbert space, which in turn lead to three distinct choices of tensionless vacua. We analyse these vacua in detail, commenting on various aspects like the central charges and the spectrum around each of them. [ABSTRACT FROM AUTHOR]

We argue that generic field theories defined on null manifolds should have an emergent BMS or conformal Carrollian structure. We then focus on a simple interacting conformal Carrollian theory, viz. Carrollian scalar electrodynamics. We look at weak (on-shell) and strong invariance (off-shell) of its equations of motion under conformal Carrollian symmetries. Helmholtz conditions are necessary and sufficient conditions for a set of equations to arise from a Lagrangian. We investigate whether the equations of motion of Carrollian scalar electrodynamics satisfy these conditions. Then we proposed an action for the electric sector of the theory. This action is the first example for an interacting conformal Carrollian Field Theory. The proposed action respects the finite and infinite conformal Carrollian symmetries in d = 4. We calculate conserved charges corresponding to these finite and infinite symmetries and then rewrite the conserved charges in terms of the canonical variables. We finally compute the Poisson brackets for these charges and confirm that infinite Carrollian conformal algebra is satisfied at the level of charges. [ABSTRACT FROM AUTHOR]

We compute the leading corrections to the Bekenstein-Hawking entropy of the Flat Space Cosmological (FSC) solutions in 3D flat spacetimes, which are the flat analogues of the BTZ black holes in AdS. The analysis is done by a computation of density of states in the dual 2D Galilean Conformal Field Theory and the answer obtained by this matches with the limiting value of the expected result for the BTZ inner horizon entropy as well as what is expected for a generic thermodynamic system. Along the way, we also develop other aspects of holography of 3D flat spacetimes. [ABSTRACT FROM AUTHOR]

We make a detailed study of the infinite dimensional Galilean Conformal Algebra (GCA) in the case of two spacetime dimensions. Classically, this algebra is precisely obtained from a contraction of the generators of the relativistic conformal symmetry in 2 d. Here we find quantum mechanical realisations of the (centrally extended) GCA by considering scaling limits of certain 2d CFTs. These parent CFTs are non-unitary and have their left and right central charges become large in magnitude and opposite in sign. We therefore develop, in parallel to the usual machinery for 2 d CFT, many of the tools for the analysis of the quantum mechanical GCA. These include the representation theory based on GCA primaries, Ward identities for their correlation functions and a nonrelativistic Kac table. In particular, the null vectors of the GCA lead to differential equations for the four point function. The solution to these equations in the simplest case is explicitly obtained and checked to be consistent with various requirements. [ABSTRACT FROM AUTHOR]

We perform a detailed analysis of Galilean field theories, starting with free theories and then interacting theories. We consider non-relativistic versions of massless scalar and Dirac field theories before we go on to review our previous construction of Galilean Electrodynamics and Galilean Yang-Mills theory. We show that in all these cases, the field theories exhibit non-relativistic conformal structure (in appropriate dimensions). The surprising aspect of the analysis is that the non-relativistic conformal structure exhibited by these theories, unlike relativistic conformal invariance, becomes infinite dimensional even in spacetime dimensions greater than two. We then couple matter with Galilean gauge theories and show that there is a myriad of different sectors that arise in the non-relativistic limit from the parent relativistic theories. In every case, if the parent relativistic theory exhibited conformal invariance, we find an infinitely enhanced Galilean conformal invariance in the non-relativistic case. This leads us to suggest that infinite enhancement of symmetries in the non-relativistic limit is a generic feature of conformal field theories in any dimension. [ABSTRACT FROM AUTHOR]