Four-point functions of the stress tensor and conserved currents inAdS4/CFT3

Abstract

We compute four point functions of the stress tensor and conserved currents in AdS 4 /CFT 3 using bulk perturbation theory. We work at treel level in the bulk theory, which we take to be either pure gravity or Yang Mills theory in AdS. We bypass the tedious evaluation of Witten diagrams using recently developed recursion relations for these correlators. In this approach, the four point function is obtained as the sum of residues of a rational function at easily identifiable poles. We write down an explicit formula for the four point correlator with arbitrary external helicities and momenta. We verify that, precisely as conjectured in a companion paper, the Maximally Helicity Violating (MHV) amplitude of gravitons or gluons appears as the coefficient of a specified singularity in the MHV stress-tensor or current correlator. We comment on the remarkably simple analytic structure of our answers in momentum space.

On the four-point function of the stress-energy tensors in a CFT

“…In order to avoid the notation clutter in what follows we rename g K into f I and hope this will not cause any confusion. 7 We thank Vasily Pestun for suggesting this idea.…”

“…Throughout the paper we keep all xi distinct and do not discuss those Ward Identities which involve coincident points. 2 The relation between the CFT correlators and scattering amplitudes is also discussed from the holographic point of view in [7,8].…”

“…This can be done using the following simple trick. 7 Let us rename the variables u, v into t, x and think of t as "time" and x as "space" coordinate. Next, we would like to think of (2.3) as a Cauchy problem, namely consider (2.3) as a set of algebraic equations on the "time" derivatives ∂f I /∂t which we need to express in terms of the original functions f I and spatial derivatives ∂f I /∂x.…”

Conformal invariance and the four point scalar correlator in slow-roll inflation

“…This is the statement that, in a particular limit, this correlation function reduces to the flat space scattering amplitude of four minimally coupled scalars in four dimensions! More precisely, we use the flat space limit developed in [59,60], which involves an analytic continuation of the momenta. In our context, the limit reads…”

Holographic stress tensor at finite coupling

“…12 These reasons are sufficient motivation to look at the four point functions in the general gravity theories we have considered in this paper. May be the techniques developed in [83,84] could help us out here.…”