Soft photon theorems from CFT Ward identites in the flat limit of AdS/CFT

We introduce a bosonic ambitwistor string theory in AdS space. Even though the theory is anomalous at the quantum level, one can nevertheless use it in the classical limit to derive a novel formula for correlation functions of boundary CFT operators in arbitrary space-time dimensions. The resulting construction can be treated as a natural extension of the CHY formalism for the flat-space S-matrix, as it similarly expresses tree-level amplitudes in AdS as integrals over the moduli space of Riemann spheres with punctures. These integrals localize on an operator-valued version of scattering equations, which we derive directly from the ambitwistor string action on a coset manifold. As a testing ground for this formalism we focus on the simplest case of ambitwistor string coupled to two cur- rent algebras, which gives bi-adjoint scalar correlators in AdS. In order to evaluate them directly, we make use of a series of contour deformations on the moduli space of punctured Riemann spheres and check that the result agrees with tree level Witten diagram computations to all multiplicity. We also initiate the study of eigenfunctions of scattering equations in AdS, which interpolate between conformal partial waves in different OPE channels, and point out a connection to an elliptic deformation of the Calogero-Sutherland model.

Section: Jhep11(2020)158mentioning

confidence: 89%

Scattering equations in AdS: scalar correlators in arbitrary dimensions

Eberhardt

Komatsu

Mizera

2020

“…We find specific corrections of the soft photon mode and gauge parameter that provide a Ward identity equivalent to the classical soft photon theorem up to 1/l 2 corrections. It has recently been demonstrated that conformal Ward identities are equivalent to the Weinberg's soft theorems defined on a flat spacetime patch resulting from the l → ∞ limit on asymptotically AdS spacetimes [30]. Our Ward identity result has a natural interpretation of being defined at "null infinity" on this patch near the center of AdS [30,31], providing the leading 1/l 2 corrections.…”

Section: Jhep08(2021)105mentioning

confidence: 70%

“…In the limit of l → ∞, we can identify an asymptotically flat patch close to the origin of the AdS spacetime [45] that has recently been used to demonstrate the equivalence of the asymptotically flat spacetime large gauge Ward identity with a CFT Ward identity [30].…”

Section: Jhep08(2021)105mentioning

confidence: 99%

Soft photon theorem in the small negative cosmological constant limit

Banerjee

Fernandes

Mitra

2021

We study the effect of electromagnetic interactions on the classical soft theorems on an asymptotically AdS background in 4 spacetime dimensions, in the limit of a small cosmological constant or equivalently a large AdS radius l. This identifies 1/l2 perturbative corrections to the known asymptotically flat spacetime leading and subleading soft factors. Our analysis is only valid to leading order in 1/l2. The leading soft factor can be expected to be universal and holds beyond tree level. This allows us to derive a 1/l2 corrected Ward identity, following the known equivalence between large gauge Ward identities and soft theorems in asymptotically flat spacetimes.

“…The goal is to gain insight into the flat spacetime limit of holography by considering the limit where the radius of curvature → ∞ from the Anti-de Sitter side, where the holographic dual is thought to be a well-defined conformal field theory. Some discussion of the viewpoint has appeared in [11,12].…”

Section: Calculationsmentioning

confidence: 99%

“…The goal of the present work is to study these quantities as a limit of asymptotically anti-de Sitter spacetimes where one may gain additional insight via the anti-de Sitter/conformal field theory correspondence. Some initial works in this direction are [11,12]. It has been shown that the BMS algebra generalizes to a Lie algebroid in asymptotically anti-de Sitter spacetime [13,14].…”

Section: Introductionmentioning

confidence: 99%

BMS symmetry via AdS/CFT

Lowe

Ramirez

2021

With a view to understanding extended-BMS symmetries in the framework of the AdS4/CFT3 correspondence, asymptotically AdS geometries are constructed with null impulsive shockwaves involving a discontinuity in superrotation parameters. The holographic dual is proposed to be a two-dimensional Euclidean defect conformal field localized on a particular timeslice in a three-dimensional conformal field theory on de Sitter spacetime. The defect conformal field theory generates a natural action of the Virasoro algebra. The large radius of curvature limit ℓ → ∞ yields spacetimes with nontrivial extended-BMS charges corresponding to a single set of Virasoro charges.