Abstract
We study non-planar correlators in mathcal{N} = 4 super-Yang-Mills in Mellin space. We focus in the stress tensor four-point correlator to order 1/N4 and in a strong coupling expansion. This can be regarded as the genus-one four-point graviton amplitude of type IIB string theory on AdS5× S5 in a low energy expansion. Both the loop supergravity result as well as the tower of stringy corrections have a remarkable simple structure in Mellin space, making manifest important properties such as the correct flat space limit and the structure of UV divergences.
Highlights
Explicit computation to seven loops is still out of reach, and the presence of UV divergences still a matter of debate, the computation of [4] shows that UV divergences are present at five loops for D = 24/5
We study non-planar correlators in N = 4 super-Yang-Mills in Mellin space
In the present paper we have studied non-planar corrections to the stress-tensor four-point correlator in N = 4 SYM, to order 1/c2 and in a large ’t Hooft coupling expansion. We have studied such correlator in Mellin space, showing that it displays a remarkable simple structure
Summary
N = 4 SYM possesses a tower of half-BPS operators Op, with p = 2, 3, · · · , of dimension ∆ = p and transforming in the [0, p, 0] representation of the SU(4) R-symmetry group. Gpshort(U, V, α, α) does not depend on the coupling constant and can be computed following [25]. For this class of correlators superconformal Ward identities fix completely the. The explicit expression for the superconformal blocks in given in appendix A We will study this correlator in a double expansion. Each term around large ’t Hooft coupling λ In this regime the intermediate operators are double trace operators labelled by their spin and n = 0, 1, · · · , with dimension.
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