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$20'$ Five-Point Function of $\mathcal{N}=4$ SYM and Stringy Corrections

Joao Vilas Boas

TL;DR

The paper develops a Mellin-space bootstrap to compute the first stringy correction to the five-point correlator of $20'$ operators in $ ext{N}=4 ext{ SYM}$ at large $N$ and strong coupling, arising from the $R^4$ interaction. By combining Mellin-space factorization with two supersymmetric twists (Drukker-Plefka and chiral algebra) and a flat-space limit argument, the authors fix almost all coefficients of the ansatz, leaving only two regular-term coefficients; these are subsequently fixed by a mild high-energy scaling assumption tied to the 10d flat-space amplitude. The final result expresses the corrected Mellin amplitude as a sum over pentagonal and triangular R-symmetry structures, with explicit decompositions and the full set of coefficients available in ancillary materials; the analysis also yields the first stringy corrections to certain four-point correlators with a current or stress tensor. Overall, this work demonstrates a powerful bootstrap approach for higher-point holographic correlators, yields new CFT data up to $igO(1/ ilde{ ext{lambda}}^{3/2})$, and opens avenues for extending these methods to higher-point functions, loop corrections, and other holographic theories.

Abstract

We setup a bootstrap approach to compute the first stringy correction to the supergravity regime of the correlation function of five $20'$ operators in $\mathcal{N}=4$ super Yang-Mills. We use factorization of Mellin amplitudes and supersymmetric constraints to fix almost completely our ansatz. The two last coefficients are fixed by a justified mild assumption based on the flat-space limit of the Mellin amplitude. As a byproduct of our analysis, we also compute the first stringy correction to the four-point correlators of three $20'$ operators and either one R-symmetry current or one stress tensor.

$20'$ Five-Point Function of $\mathcal{N}=4$ SYM and Stringy Corrections

TL;DR

The paper develops a Mellin-space bootstrap to compute the first stringy correction to the five-point correlator of operators in at large and strong coupling, arising from the interaction. By combining Mellin-space factorization with two supersymmetric twists (Drukker-Plefka and chiral algebra) and a flat-space limit argument, the authors fix almost all coefficients of the ansatz, leaving only two regular-term coefficients; these are subsequently fixed by a mild high-energy scaling assumption tied to the 10d flat-space amplitude. The final result expresses the corrected Mellin amplitude as a sum over pentagonal and triangular R-symmetry structures, with explicit decompositions and the full set of coefficients available in ancillary materials; the analysis also yields the first stringy corrections to certain four-point correlators with a current or stress tensor. Overall, this work demonstrates a powerful bootstrap approach for higher-point holographic correlators, yields new CFT data up to , and opens avenues for extending these methods to higher-point functions, loop corrections, and other holographic theories.

Abstract

We setup a bootstrap approach to compute the first stringy correction to the supergravity regime of the correlation function of five operators in super Yang-Mills. We use factorization of Mellin amplitudes and supersymmetric constraints to fix almost completely our ansatz. The two last coefficients are fixed by a justified mild assumption based on the flat-space limit of the Mellin amplitude. As a byproduct of our analysis, we also compute the first stringy correction to the four-point correlators of three operators and either one R-symmetry current or one stress tensor.

Paper Structure

This paper contains 15 sections, 112 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Setup
  3. Mellin space
  4. Factorization of Mellin amplitudes
  5. OPE exchanges and four-point correlators
  6. The bootstrap
  7. The ansatz
  8. Factorization
  9. Drukker-Plefka twist
  10. Chiral Algebra twist
  11. Flat-space Limit
  12. Result
  13. Discussion
  14. Four-point correlators
  15. D-functions

Figures (2)

  • Figure 1: R-symmetry structures with one and two cycles. Each line between points $i$ and $j$ corresponds to a factor of $t_{ij}$. The number of independent structures is determined by the number of ways to distribute the points into the cycles modulo invariance under cyclic permutations and reflections.
  • Figure 2: Factorization of a Mellin amplitude with $n=5$ and $k=2$. The poles of the Mellin amplitude are associated with the OPE exchange of single-trace operators of twist $\tau$. The residues are related to lower-point functions $M_L$ and $M_R$.