Handling Handles: Nonplanar Integrability in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory

TL;DR

This paper introduces a novel integrability framework for calculating nonplanar correlation functions in $ ext{N}=4$ supersymmetric Yang-Mills theory, extending the computational reach beyond the planar limit and testing it at one and two loops.

Contribution

It presents a new integrability setup that polygonizes, hexagonizes, and incorporates mirror particles to compute nonplanar correlators at any coupling order.

Findings

Successfully tested against non-planar four-point correlators at one and two loops.

Provides a systematic method for higher-order genus expansion calculations.

Extends integrability techniques beyond the planar limit.

Abstract

We propose an integrability setup for the computation of correlation functions of gauge-invariant operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory at higher orders in the large $N_{\text{c}}$ genus expansion and at any order in the 't Hooft coupling $g_{\text{YM}}^2N_{\text{c}}$. In this multi-step proposal, one polygonizes the string worldsheet in all possible ways, hexagonalizes all resulting polygons, and sprinkles mirror particles over all hexagon junctions to obtain the full correlator. We test our integrability-based conjecture against a non-planar four-point correlator of large half-BPS operators at one and two loops.