Landau diagrams in AdS and S-matrices from conformal correlators

Self Cite

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: 98%

Section: Jhep11(2020)158mentioning

confidence: 99%

Scattering equations in AdS: scalar correlators in arbitrary dimensions

Eberhardt

Komatsu

Mizera

2020

Self Cite

“…In unpublished work from 2017, while studying the flat space limit of general multi-point functions of gapped QFT's in AdS, Shota Komatsu has solved similar problems; see in particular[9]. We thank Shota for several insightful discussions on this point.…”

mentioning

confidence: 88%

“…A similar observation holds for the (Σ − 1) 3 contribution. 9 In addition, the overall degree of V (1,2) w.r.t.s andt is expected to be at most second order, i.e. it should not exceed the degree of the top term.…”

Section: Towards the Full Amplitude: ζ 3 And ζmentioning

confidence: 99%

Large p explorations. From SUGRA to big STRINGS in Mellin space

Aprile

Vieira

2020

We explore a new way of probing scattering of closed strings in AdS5×S5, which we call ‘the large p limit’. It consists of studying four-point correlators of single-particle operators in $$ \mathcal{N} $$ N = 4 SYM at large N and large ’t Hooft coupling λ, by looking at the regime in which the dual KK modes become short massive strings. In this regime the charge of the single-particle operators is order λ1/4 and the dual KK modes are in between fields and strings. Starting from SUGRA we compute the large p limit of the correlators by introducing an improved AdS5×S5 Mellin space amplitude, and we show that the correlator is dominated by a saddle point. Our results are consistent with the picture of four geodesics shooting from the boundary of AdS5×S5 towards a common bulk point, where they scatter as if they were in flat space. The Mandelstam invariants are put in correspondence with the Mellin variables and in turn with certain combinations of cross ratios. At the saddle point the dynamics of the correlator is directly related to the bulk Mellin amplitude, which in the process of taking large p becomes the flat space ten-dimensional S-matrix. We thus learn how to embed the full type IIB S-matrix in the AdS5×S5 Mellin amplitude, and how to stratify the latter in a large p expansion. We compute the large p limit of all genus zero data currently available, pointing out additional hidden simplicity of known results. We then show that the genus zero resummation at large p naturally leads to the Gross-Mende phase for the minimal area surface around the bulk point. At one-loop, we first uncover a novel and finite Mellin amplitude, and then we show that the large p limit beautifully asymptotes the gravitational S-matrix.

“…Indeed the i prescription effectively tells us that we need to perform an analytic continuation even to work at physical values of parameters. In particular, we see from (3.16), 38 theH(a) is actually a function of the combination of variables a = a + i˜ (3.21) for an appropriate definition of˜ > 0. It is useful to viewH as a function ofã.…”

Section: Jhep05(2021)143mentioning

confidence: 99%

Bounds on Regge growth of flat space scattering from bounds on chaos

Chandorkar¹,

Chowdhury

Kundu

et al. 2021

We study four-point functions of scalars, conserved currents, and stress tensors in a conformal field theory, generated by a local contact term in the bulk dual description, in two different causal configurations. The first of these is the standard Regge configuration in which the chaos bound applies. The second is the ‘causally scattering configuration’ in which the correlator develops a bulk point singularity. We find an expression for the coefficient of the bulk point singularity in terms of the bulk S matrix of the bulk dual metric, gauge fields and scalars, and use it to determine the Regge scaling of the correlator on the causally scattering sheet in terms of the Regge growth of this S matrix. We then demonstrate that the Regge scaling on this sheet is governed by the same power as in the standard Regge configuration, and so is constrained by the chaos bound, which turns out to be violated unless the bulk flat space S matrix grows no faster than s2 in the Regge limit. It follows that in the context of the AdS/CFT correspondence, the chaos bound applied to the boundary field theory implies that the S matrices of the dual bulk scalars, gauge fields, and gravitons obey the Classical Regge Growth (CRG) conjecture.