Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On Genus-one String Amplitudes on $AdS_5 \times S^5$

Luis F. Alday

TL;DR

This work probes non-planar corrections to the stress-tensor four-point correlator in N=4 SYM at strong coupling, recasting the genus-one AdS amplitude in Mellin space. It develops a unified framework where loop effects split into loop supergravity, governed by simultaneous poles in $s,t,u$, and stringy corrections, determined from tree-level data, via a constructive unitarity-inspired procedure. UV divergences are interpreted as Mellin sums that require regularization, with polynomial ambiguities constrained by analyticity in spin and the flat-space limit, which matches the known genus-one 10D string amplitude. The results illuminate the AdS/CFT dictionary at genus one, clarify the flat-space limit, and pave the way for extensions to broader correlators and higher-genus corrections within the Mellin-Polyakov bootstrap program.

Abstract

We study non-planar correlators in ${\cal N}=4$ super-Yang-Mills in Mellin space. We focus in the stress tensor four-point correlator to order $1/N^4$ and in a strong coupling expansion. This can be regarded as the genus-one four-point graviton amplitude of type IIB string theory on $AdS_5 \times S^5$ 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.

On Genus-one String Amplitudes on $AdS_5 \times S^5$

TL;DR

This work probes non-planar corrections to the stress-tensor four-point correlator in N=4 SYM at strong coupling, recasting the genus-one AdS amplitude in Mellin space. It develops a unified framework where loop effects split into loop supergravity, governed by simultaneous poles in , and stringy corrections, determined from tree-level data, via a constructive unitarity-inspired procedure. UV divergences are interpreted as Mellin sums that require regularization, with polynomial ambiguities constrained by analyticity in spin and the flat-space limit, which matches the known genus-one 10D string amplitude. The results illuminate the AdS/CFT dictionary at genus one, clarify the flat-space limit, and pave the way for extensions to broader correlators and higher-genus corrections within the Mellin-Polyakov bootstrap program.

Abstract

We study non-planar correlators in super-Yang-Mills in Mellin space. We focus in the stress tensor four-point correlator to order and in a strong coupling expansion. This can be regarded as the genus-one four-point graviton amplitude of type IIB string theory on 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.

Paper Structure

This paper contains 16 sections, 101 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Geralities and structure at tree level
  3. Generalities
  4. Structure at tree level
  5. Structure at one loop
  6. Unitarity method on $AdS$
  7. Loop supergravity
  8. Flat space limit
  9. Stringy corrections
  10. Regularisation, UV divergences and ambiguities
  11. Summary: full structure at one-loop
  12. Conclusions
  13. A basis for polynomial Mellin amplitudes
  14. Inverting polynomial Mellin amplitudes
  15. Double-discontinuity of loop supergravity
  16. ...and 1 more sections

Figures (2)

  • Figure :
  • Figure :