Color/kinematics duality in AdS4

We explore color-kinematic duality for tree-level AdS/CFT correlators in momentum space. We start by studying the bi-adjoint scalar in AdS at tree-level as an illustrative example. We follow this by investigating two forms of color-kinematic duality in Yang-Mills theory, the first for the integrated correlator in AdS4 and the second for the integrand in general AdSd+1. For the integrated correlator, we find color-kinematics does not yield additional relations among n-point, color-ordered correlators. To study color-kinematics for the AdSd+1 Yang-Mills integrand, we use a spectral representation of the bulk-to-bulk propagator so that AdS diagrams are similar in structure to their flat space counterparts. Finally, we study color KLT relations for the integrated correlator and double-copy relations for the AdS integrand. We find that double-copy in AdS naturally relates the bi-adjoint theory in AdSd+3 to Yang-Mills in AdSd+1. We also find a double-copy relation at three-points between Yang-Mills in AdSd+1 and gravity in AdSd−1 and comment on the higher-point generalization. By analytic continuation, these results on AdS/CFT correlators can be translated into statements about the wave function of the universe in de Sitter.

Section: Jhep03(2021)249supporting

confidence: 78%

“…The same transformation was found in[50] 7. One can also check that the AdS color-ordered correlators satisfy the same U(1) decoupling identity as their flat space counterparts.…”

supporting

confidence: 53%

See 1 more Smart Citation

On duality of color and kinematics in (A)dS momentum space

Albayrak

Kharel

Meltzer

2021

“…This relation gives an AdS version of the color-kinematic duality, which is literally the same as that of the flat space gluons! Finding AdS extensions of the flat space color-kinematic duality was also discussed recently in momentum space [78,79]. However, our realization of this duality in Mellin space appears to be the simplest and bears most resemblance to the flat space relation.…”

Section: Jhep06(2021)020supporting

confidence: 66%

Gluon scattering in AdS from CFT

Alday

Behan

Ferrero

et al. 2021

153

We present a systematic study of holographic correlators in a vast array of SCFTs with non-maximal superconformal symmetry. These theories include 4d $$ \mathcal{N} $$ N = 2 SCFTs from D3-branes near F-theory singularities, 5d Seiberg exceptional theories and 6d E-string theory, as well as 3d and 4d phenomenological models with probe flavor branes. We consider current multiplets and their generalizations with higher weights, dual to massless and massive super gluons in the bulk. At leading order in the inverse central charge expansion, connected four-point functions of these operators correspond to tree-level gluon scattering amplitudes in AdS. We show that all such tree-level four-point amplitudes in all these theories are fully fixed by symmetries and consistency conditions and explicitly construct them. Our results encode a wealth of SCFT data and exhibit various interesting emergent structures. These include Parisi-Sourlas-like dimensional reductions, hidden conformal symmetry and an AdS version of the color-kinematic duality.

“…For example, there has been progress in the study of on-shell recursion relations [44][45][46][47], positive geometries [48], and the ambitwistor string [49,50] for (A)dS correlators. Requiring that AdS correlators factorize correctly when we put propagators on shell also gives a useful consistency check for new conjectures, including on the possible generalization of double-copy [51] to AdS/CFT correlators [52][53][54][55].…”

Section: Introductionmentioning

confidence: 99%

Dispersion formulas in QFTs, CFTs and holography

Meltzer

2021

We study momentum space dispersion formulas in general QFTs and their applications for CFT correlation functions. We show, using two independent methods, that QFT dispersion formulas can be written in terms of causal commutators. The first derivation uses analyticity properties of retarded correlators in momentum space. The second derivation uses the largest time equation and the defining properties of the time-ordered product. At four points we show that the momentum space QFT dispersion formula depends on the same causal double-commutators as the CFT dispersion formula. At n-points, the QFT dispersion formula depends on a sum of nested advanced commutators. For CFT four-point functions, we show that the momentum space dispersion formula is equivalent to the CFT dispersion formula, up to possible semi-local terms. We also show that the Polyakov-Regge expansions associated to the momentum space and CFT dispersion formulas are related by a Fourier transform. In the process, we prove that the momentum space conformal blocks of the causal double-commutator are equal to cut Witten diagrams. Finally, by combining the momentum space dispersion formulas with the AdS Cutkosky rules, we find a complete, bulk unitarity method for AdS/CFT correlators in momentum space.