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Abstract We ask when it is possible to construct arbitrary unitary multiplets of the superconformal algebra with eight Poincaré supercharges that are compatible with locality from (continuous deformations of) representations in free field theories. We answer this question in two, three, and five dimensions. In four dimensions, we resort to an intricate but self-consistent web of conjectures. If correct, these conjectures imply various new non-perturbative constraints on short multiplets in any local unitary 4d N $$ \mathcal{N} $$ = 2 superconformal field theory and on an unusual set of related vertex algebras. Throughout, we connect our results with properties of deformations in the space of theories.

Abstract We consider a 1 2 $$ \frac{1}{2} $$ -BPS solution for a D3 brane probe in AdS5 × S 5 that has world-volume geometry of AdS3 × S 1. It intersects the boundary over a surface that represents a dimension 2 defect in the boundary N $$ \mathcal{N} $$ = 4 SYM theory. The effective action of the probe brane is proportional to the logarithmically divergent volume of AdS3 and may thus be interpreted as computing conformal anomaly of supersymmetric S 2 defect. The classical action scales as N. We compute the 1-loop correction to it due to quantum fluctuations of the D3 brane world-volume fields and compare the result to an earlier suggested expression for the defect anomaly. We also perform a similar analysis of a 1 2 $$ \frac{1}{2} $$ -BPS M5 brane probe solution in AdS7 × S 4 with the world-volume geometry of AdS5 × S 1 that represents a dimension 4 defect in the boundary (2,0) 6d theory. Here the classical M5 brane action computes the leading order N 2 term in a-anomaly of the supersymmetric S 4 defect. We perform a detailed computation of the 1-loop correction to the M5 brane effective action and thus provide a prediction for the subleading constant in the S 4 defect a-anomaly coefficient.

Abstract We consider a family of Argyres-Douglas theories, which are 4D N $$ \mathcal{N} $$ = 2 strongly coupled superconformal field theories (SCFTs) but share many features with 4D N $$ \mathcal{N} $$ = 4 super-Yang-Mills theories. In particular, the two central charges of these theories are the same, namely a = c. We derive a simple and illuminating formula for the Schur index of these theories, which factorizes into the product of a Casimir term and a term referred to as the Schur partition function. While the former is controlled by the anomaly, the latter is identified with the vacuum character of the corresponding chiral algebra and is expected to satisfy the modular linear differential equation. Our simple expression for the Schur partition function, which can be regarded as the generalization of MacMahon’s generalized sum-of-divisor function, allows one to numerically compute the series expansions efficiently, and furthermore find the corresponding modular linear differential equation. In a special case where the chiral algebra is known, we are able to derive the corresponding modular linear differential equation using Zhu’s recursion relation. We further study the solutions to the modular linear differential equations and discuss their modular transformations. As an application, we study the high temperature limit or the Cardy-like limit of the Schur index using its simple expression and modular properties, thus shedding light on the 1/4-BPS microstates of genuine N $$ \mathcal{N} $$ = 2 SCFTs with a = c and their dual quantum gravity via the AdS/CFT correspondence.

Abstract We study ultraviolet (UV) incarnations of deep infrared (IR) physics on the Coulomb branch of the simplest interacting 4D N $$ \mathcal{N} $$ = 2 superconformal field theory: the minimal Argyres-Douglas (MAD) theory. One of the most basic properties of the Coulomb branch is an emergent infinite-dimensional higher-spin symmetry. While the MAD theory is interacting and therefore does not have such a symmetry, we find UV operators that encode the emergent complex higher-spin symmetry on the Coulomb branch. Moreover, we show that cousins of these UV operators give rise to cousins of the IR higher-spin multiplets. In terms of superconformal representation theory, we are led to a conjecture on the exact spectrum of C ¯ R , r j j ¯ $$ {\overline{\mathcal{C}}}_{R,r\left(j,\overline{j}\right)} $$ multiplets in the MAD theory for all R, r, j, and j ¯ $$ \overline{j} $$ satisfying R + j ¯ − j + 1 = 0 $$ R+\overline{j}-j+1=0 $$ , thereby making progress towards a full characterization of the protected spectrum. Along the way, we give a geometrical interpretation of these operators and include them in an extension of the Coulomb branch / N $$ \mathcal{N} $$ = 2 chiral operator correspondence.

Abstract Celestial holography provides a promising avenue to studying bulk scattering in flat spacetime from the perspective of boundary celestial conformal field theory (CCFT). A key ingredient in connecting the two sides is the celestial amplitude, which is given by the Mellin transform of momentum space scattering amplitude in energy. As such, celestial amplitudes can be identified with the correlation functions in celestial conformal field theory. In this paper, we introduce the further notion of celestial Mellin amplitude, which is given by the Mellin transform of celestial amplitude in coordinate. For technical reasons, we focus on the celestial Mellin amplitudes for scalar fields in three dimensional flat spacetime dual to 1D CCFT, and discuss the celestial Mellin block expansion. In particular, the poles of the celestial Mellin amplitude encode the scaling dimensions of the possible exchanged operators, while the residues there are related to the OPE coefficient squares in a linear and explicit way. We also compare the celestial Mellin amplitudes with the coefficient functions which can be obtained using inversion formulae. Finally, we make some comments about the possible generalizations of celestial Mellin amplitudes to higher dimensions.

Abstract Despite the power of supersymmetry, finding exact closed-form expressions for the protected operator spectra of interacting superconformal field theories (SCFTs) is difficult. In this paper, we take a step towards a solution for the “simplest” interacting 4D N $$ \mathcal{N} $$ = 2 SCFT: the minimal Argyres-Douglas (MAD) theory. We present two results that go beyond the well-understood Coulomb branch and Schur sectors. First, we find the exact closed-form spectrum of multiplets containing operators that are chiral with respect to any N $$ \mathcal{N} $$ = 1 ⊂ N $$ \mathcal{N} $$ = 2 superconformal subalgebra. We argue that this “full” chiral sector (FCS) is as simple as allowed by unitarity for a theory with a Coulomb branch and that, up to a rescaling of U(1) r quantum numbers and the vanishing of a finite number of states, the MAD FCS is isospectral to the FCS of the free N $$ \mathcal{N} $$ = 2 Abelian gauge theory. In the language of superconformal representation theory, this leaves only the spectrum of the poorly understood C ¯ R , r j j ¯ $$ {\overline{\mathcal{C}}}_{R,{r}_{\left(j,\overline{j}\right)}} $$ multiplets to be determined. Our second result sheds light on these observables: we find an exact closed-form answer for the number of C ¯ 0 , r j 0 $$ {\overline{\mathcal{C}}}_{0,{r}_{\left(j,0\right)}} $$ multiplets, for any r and j, in the MAD theory. We argue that this sub-sector is also as simple as allowed by unitarity for a theory with a Coulomb branch and that there is a natural map to the corresponding sector of the free N $$ \mathcal{N} $$ = 2 Abelian gauge theory. These results motivate a conjecture on the full local operator algebra of the MAD theory.

Abstract It was recently shown that the N $$ \mathcal{N} $$ = 2 string topological amplitudes in the heterotic weak coupling limit generate a six-dimensional Melvin space, providing a description of the Ω-background in string theory, where string propagation can be exactly studied. In this work, we generalise the analysis to the refined case of the Ω-background with two independent deformation parameters. The Melvin space is now ten-dimensional and is extended by an action on the internal K3 compactification manifold of the heterotic superstring, corresponding to an SU(2) R rotation in the field theory description. We identify the class of heterotic topological amplitudes realising this background as the scattering of two anti-self-dual gravitons and arbitrary numbers of anti-self-dual graviphotons, self-dual vector fields of the dilaton multiplet, together with self-dual magnetic fluxes along the K3. In the field theory limit, our result correctly reproduces the perturbative part of the Nekrasov free energy in the case where both equivariant parameters are turned on.

Abstract Celestial operator product expansions (OPEs) arise from the collinear limit of scattering amplitudes and play a vital role in celestial holography. In this paper, we derive the celestial OPEs of massless fields in string theory from the worldsheet. By studying the worldsheet OPEs of vertex operators in worldsheet CFT and further examining their behaviors in the collinear limit, we find that new vertex operators for the massless fields in string theory are generated and become dominant in the collinear limit. Mellin transforming to the conformal basis yields exactly the celestial OPEs in celestial CFT. We also derive the celestial OPEs from the collinear factorization of string amplitudes and the results derived in these two different methods are in perfect agreement with each other. Our final formulae of celestial OPEs are applicable to general dimensions, corresponding to Einstein-Yang-Mills theory supplemented by some possible higher derivative interactions. Specializing to 4D, we reproduce all the celestial OPEs for gluon and graviton in the literature. We consider various string theories, including the open and closed bosonic string, as well as the closed superstring theory with N $$ \mathcal{N} $$ = 1 and N $$ \mathcal{N} $$ = 2 worldsheet supersymmetry. In the case of N $$ \mathcal{N} $$ = 2 string, we also derive all the SL 2 ℝ ¯ $$ \overline{\mathrm{SL}\left(2,\mathbb{R}\right)} $$ descendant contributions in the celestial OPE; the soft sector of such OPE just yields the w 1+∞ algebra after rewriting in terms of chiral modes. Our stringy derivation of celestial OPEs thus initiates the first step towards the microscopic realization of celestial CFT dual to string theory in flat spacetime.

Abstract Celestial holography promisingly reformulates the scattering amplitude holographically in terms of celestial conformal field theory living at null infinity. Recently, an infinite-dimensional symmetry algebra was discovered in Einstein-Yang-Mills theory. The starting point in the derivation is the celestial OPE of two soft currents, and the key ingredient is the summation of SL 2 ℝ ¯ $$ \overline{\mathrm{SL}\left(2,\mathbb{R}\right)} $$ descendants in OPE. In this paper, we consider the supersymmetric Einstein-Yang-Mills theory and obtain the supersymmetric extension of the holographic symmetry algebra. Furthermore, we derive infinitely many Ward identities associated with the infinite soft currents which generate the holographic symmetry algebra. This is realized by considering the OPE between a soft symmetry current and a hard operator, and then summing over its SL 2 ℝ ¯ $$ \overline{\mathrm{SL}\left(2,\mathbb{R}\right)} $$ descendants. These Ward identities reproduce the known Ward identities corresponding to the leading, sub-leading, and sub-sub-leading soft graviton theorems as well as the leading and sub-leading soft gluon theorems. By performing shadow transformations, we also obtain infinitely many shadow Ward identities, including the stress tensor Ward identities for sub-leading soft graviton. Finally, we use our procedure to discuss the corrections to Ward identities in effective field theory (EFT), and reproduce the corrections to soft theorems at sub-sub-leading order for graviton and sub-leading order for photon. For this aim, we derive general formulae for the celestial OPE and its corresponding Ward identities arising from a cubic interaction of three spinning massless particles. Our formalism thus provides a unified framework for understanding the Ward identities in celestial conformal field theory, or equivalently the soft theorems in scattering amplitude.

Abstract We systematically study 4D N $$ \mathcal{N} $$ = 2 superconformal field theories (SCFTs) that can be constructed via type IIB string theory on isolated hypersurface singularities (IHSs) embedded in ℂ4. We show that if a theory in this class has no N $$ \mathcal{N} $$ = 2-preserving exactly marginal deformation (i.e., the theory is isolated as an N $$ \mathcal{N} $$ = 2 SCFT), then it has no 1-form symmetry. This situation is somewhat reminiscent of 1-form symmetry and decomposition in 2D quantum field theory. Moreover, our result suggests that, for theories arising from IHSs, 1-form symmetries originate from gauge groups (with vanishing beta functions). One corollary of our discussion is that there is no 1-form symmetry in IHS theories that have all Coulomb branch chiral ring generators of scaling dimension less than two. In terms of the a and c central charges, this condition implies that IHS theories satisfying a < 1 24 15 r + 2 f $$ a

Abstract Celestial amplitude is a new reformulation of momentum space scattering amplitudes and offers a promising way for flat holography. In this paper, we study the celestial amplitudes in N $$ \mathcal{N} $$ = 4 Super-Yang-Mills (SYM) theory aiming at understanding the role of superconformal symmetry in celestial holography. We first construct the superconformal generators acting on the celestial superfield which assembles all the on-shell fields in the multiplet together in terms of celestial variables and Grassmann parameters. These generators satisfy the superconformal algebra of N $$ \mathcal{N} $$ = 4 SYM theory. We also compute the three-point and four-point celestial super-amplitudes explicitly. They can be identified as the conformal correlation functions of the celestial superfields living at the celestial sphere. We further study the soft and collinear limits which give rise to the super-Ward identity and super-OPE on the celestial sphere, respectively. Our results initiate a new perspective of understanding the well-studied N $$ \mathcal{N} $$ = 4 SYM amplitudes via 2D celestial conformal field theory.

Abstract We propose a holographic entanglement entropy prescription for general states and regions in two models of holography beyond AdS/CFT known as flat3/BMSFT and (W)AdS3/WCFT. Flat3/BMSFT is a candidate of holography for asymptotically flat three- dimensional spacetimes, while (W)AdS3/WCFT is relevant in the study of black holes in the real world. In particular, the boundary theories are examples of quantum field theories that feature an infinite dimensional symmetry group but break Lorentz invariance. Our holographic entanglement entropy proposal is given by the area of a swing surface that consists of ropes, which are null geodesics emanating from the entangling surface at the boundary, and a bench, which is a spacelike geodesic connecting the ropes. The proposal is supported by an extension of the Lewkowycz-Maldacena argument, reproduces previous results based on the Rindler method, and satisfies the first law of entanglement entropy.

Abstract We study several aspects of holographic entanglement in two models known as flat3/BMSFT and (W)AdS3/WCFT. These are two examples of holography beyond AdS/CFT where the boundary field theories are not Lorentz invariant but still feature an infinite set of local symmetries. In the first example, BMS-invariant field theories (BMSFTs) are conjectured to provide a holographic description of quantum gravity in asymptotically flat three-dimensional spacetimes; while in the second example, warped conformal field theories (WCFTs) are proposed to describe quantum gravity in warped AdS3 or AdS3 backgrounds with Dirichlet-Neumann boundary conditions. In particular, we derive the modular Hamiltonian for single intervals in both BMSFTs and WCFTs and find the holographic duals in the bulk using the covariant formulation of gravitational charges. We also extend the first law of entanglement entropy to these models of non-AdS holography and discuss the bound on “modular chaos” introduced recently in the context of the AdS/CFT correspondence.

Abstract A necessary condition for partial breaking of N $$ \mathcal{N} $$ = 2 global supersymmetry is the presence of nonlinear deformations of the field transformations which cannot be generated by background values of auxiliary fields. This work studies the simplest of these deformations which already occurs in N $$ \mathcal{N} $$ = 1 global supersymmetry, and its coupling to supergravity. It can be viewed as an imaginary constant shift of the D-auxiliary real field of an abelian gauge multiplet. We show how this deformation describes the magnetic dual of a Fayet-Iliopoulos term, a result that remains valid in supergravity, using its new-minimal formulation. Local supersymmetry and the deformation induce a positive cosmological constant. Moreover, the deformed U(1) Maxwell theory coupled to supergravity describes upon elimination of the auxiliary fields the gauging of R-symmetry, realised by the Freedman model of 1976. To this end, we construct the chiral spinor multiplet in superconformal tensor calculus by working out explicitly its transformation rules and use it for an alternative description of the new-minimal supergravity coupled to a U(1) multiplet. We also discuss the deformed Maxwell theory in curved superspace.

Abstract Boundary correlators of elementary fields in some 2d conformal field theories defined on AdS2 have a particularly simple structure. For example, the correlators of the Liouville scalar happen to be the same as the correlators of the chiral component of the stress tensor on a plane restricted to the real line. Here we show that an analogous relation is true also in the WZW model: boundary correlators of the WZW scalars have the same structure as the correlators of chiral Kac-Moody currents. This is checked at the level of the tree and one-loop Witten diagrams in AdS2. We also compute some tree-level correlators in a generic σ-model defined on AdS2 and show that they simplify only in the WZW case where an extra Kac-Moody symmetry appears. In particular, the terms in 4- point correlators having logarithmic dependence on 1d cross-ratio cancel only at the WZW point. One motivation behind this work is to learn how to compute AdS2 loop corrections in 2d models with derivative interactions related to the study of correlators of operators on Wilson loops in string theory in AdS.

Abstract We study the Dirac-Born-Infeld (DBI) action with one linear and one nonlinear supersymmetry in the presence of a constant Fayet-Iliopoulos (FI) D-term added explicitly or through a deformation of supersymmetry transformations. The linear supersymmetry appears to be spontaneously broken since the D auxiliary field gets a non- vanishing vacuum expectation value and an extra term proportional to the FI parameter involving fermions emerges in the non-linear formulation of the action written recently. However in this note, we show that on-shell this action is equivalent to a standard supersymmetric DBI action without FI term but with redefined tension, at least up to order of mass-dimension 12 effective interactions.

Abstract We explore the J T ¯ $$ \overline{T} $$ and T J ¯ $$ \overline{J} $$ deformations of two-dimensional field theories possessing N $$ \mathcal{N} $$ = (0, 1), (1, 1) and (0, 2) supersymmetry. Based on the stress-tensor and flavor current multiplets, we construct various bilinear supersymmetric primary operators that induce the J T ¯ $$ \overline{T} $$ /T J ¯ $$ \overline{J} $$ deformation in a manifestly supersymmetric way. Moreover, their supersymmetric descendants are shown to agree with the conventional J T ¯ $$ \overline{T} $$ /T J ¯ $$ \overline{J} $$ operator on-shell. We also present some examples of J T ¯ $$ \overline{T} $$ /T J ¯ $$ \overline{J} $$ flows arising from the supersymmetric deformation of free theories. Finally, we observe that all the deformation operators fit into a general pattern which generalizes the Smirnov-Zamolodchikov type composite operators.

Abstract The T T ¯ $$ T\overline{T} $$ deformation of a supersymmetric two-dimensional theory preserves the original supersymmetry. Moreover, in several interesting cases the deformed theory possesses additional non-linearly realized supersymmetries. We show this for certain N $$ \mathcal{N} $$ = (2, 2) models in two dimensions, where we observe an intriguing similarity with known N $$ \mathcal{N} $$ = 1 models in four dimensions. This suggests that higher-dimensional models with non-linearly realized supersymmetries might also be obtained from T T ¯ $$ T\overline{T} $$ -like flow equations. We show that in four dimensions this is indeed the case for N $$ \mathcal{N} $$ = 1 Born-Infeld theory, as well as for the Goldstino action for spontaneously broken N $$ \mathcal{N} $$ = 1 supersymmetry.

Abstract In a series of recent papers, a special kind of AdS2/CFT1 duality was observed: the boundary correlators of elementary fields that appear in the Lagrangian of a 2d conformal theory in rigid AdS2 background are the same as the correlators of the corresponding primary operators in the chiral half of that 2d CFT in flat space restricted to the real line. The examples considered were: (i) the Liouville theory where the operator dual to the Liouville scalar in AdS2 is the stress tensor; (ii) the abelian Toda theory where the operators dual to the Toda scalars are the W $$ \mathcal{W} $$ -algebra generators; (iii) the non-abelian Toda theory where the Liouville field is dual to the stress tensor while the extra gauged WZW theory scalars are dual to non-abelian parafermionic operators. By direct Witten diagram com- putations in AdS2 one can check that the structure of the boundary correlators is indeed consistent with the Virasoro (or higher) symmetry. Here we consider a supersymmetric generalization: the N $$ \mathcal{N} $$ = 1 superconformal Liouville theory in AdS2. We start with the super Liouville theory coupled to 2d supergravity and show that a consistent restriction to rigid AdS2 background requires a non-zero value of the supergravity auxiliary field and thus a modification of the Liouville potential from its familiar flat-space form. We show that the Liouville scalar and its fermionic partner are dual to the chiral half of the stress tensor and the supercurrent of the super Liouville theory on the plane. We perform tests supporting the duality by explicitly computing AdS2 Witten diagrams with bosonic and fermionic loops.

Abstract We explore the emergence of gravitation from entanglement in holographic CFTs with gravitational anomalies. More specifically, the holographic correspondence between topologically massive gravity (TMG) with gravitational Chern-Simons term in the 3D bulk and its dual CFT with unbalanced left and right moving central charges on the 2D boundary, is studied from the quantum entanglement perspective. Using the first law of entanglement, we derive the holographic dictionary of the energy-momentum tensor in TMG, including the chiral case with logarithmic mode. Furthermore, we show that the linearized equation of motion of TMG can also be obtained from entanglement using the Wald-Tachikawa covariant phase space formalism. Finally, we identify a quasi-local gravitational energy in the entanglement wedge as the holographic dual of relative entropy in gravitationally anomalous CFTs. The positivity and monotonicity of relative entropy imply that such a gravitational energy should be positive definite and become larger when increasing the size of the entanglement wedge. These constraints from quantum information may be potentially used to discuss the UV inconsistent issues of TMG.

Abstract It was recently observed that boundary correlators of the elementary scalar field of the Liouville theory on AdS2 background are the same (up to a non-trivial proportionality coefficient) as the correlators of the chiral stress tensor of the Liouville CFT on the complex plane restricted to the real line. The same relation generalizes to the conformal abelian Toda theory: boundary correlators of Toda scalars on AdS2 are directly related to the correlation functions of the chiral W $$ \mathcal{W} $$ -symmetry generators in the Toda CFT and thus are essentially controlled by the underlying infinite-dimensional symmetry. These may be viewed as examples of AdS2/CFT1 duality where the CFT1 is the chiral half of a 2d CFT; we shall to this as AdS 2 / CFT 2 1 2 $$ {\mathrm{AdS}}_2/{\mathrm{CFT}}_2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} $$ . In this paper we demonstrate that this duality applies also to the non-abelian Toda theory containing a Liouville scalar coupled to a 2d σ-model originating from the SL(2, ℝ)/U(1) gauged WZW model. Here the Liouville scalar is again dual to the chiral stress tensor T while the other two scalars are dual to the parafermionic operators V ± of the non-abelian Toda CFT. We explicitly check the duality at the next-to-leading order in the large central charge expansion by matching the chiral CFT correlators of (T, V +, V −) (computed using a free field representation) with the boundary correlators of the three Toda scalars given by the tree-level and one-loop Witten diagrams in AdS2.

Abstract We study the general deformation of N $$ \mathcal{N} $$ = 2 supersymmetry transformations of a vector multiplet that forms a (constant) triplet under the SU(2) R-symmetry corresponding to the magnetic dual of the triplet of the Fayet-Iliopoulos (FI) parameters. We show that in the presence of both triplets, the induced scalar potential of a vector multiplet with generic prepotential has always a minimum that realises partial breaking of N $$ \mathcal{N} $$ = 2 → N $$ \mathcal{N} $$ = 1 supersymmetry. We then consider the impact of the deformation in the Dirac-Born-Infeld (DBI) action where one supersymmetry is non-linearly realised, described by a nilpotent constraint on the deformed N $$ \mathcal{N} $$ = 2 chiral-chiral superfield. We show that the generic magnetic deformation induces an ordinary FI D-term along the linear supersymmetry via the theta-angle. Moreover, we argue that the resulting action differs on-shell from the standard one (DBI+FI) by fermionic contributions.

Abstract BMS symmetry, which is the asymptotic symmetry at null infinity of flat spacetime, is an important input for flat holography. In this paper, we give a holographic calculation of entanglement entropy and Rényi entropy in three dimensional Einstein gravity and Topologically Massive Gravity. The geometric picture for the entanglement entropy is the length of a spacelike geodesic which is connected to the interval at null infinity by two null geodesics. The spacelike geodesic is the fixed points of replica symmetry, and the null geodesics are along the modular flow. Our strategy is to first reformulate the Rindler method for calculating entanglement entropy in a general setup, and apply it for BMS invariant field theories, and finally extend the calculation to the bulk.