Handling Handles. Part II. Stratification and Data Analysis

TL;DR

This paper develops a detailed framework for computing non-planar corrections in a supersymmetric gauge theory using graph stratification, triangulations, and mirror contributions, with perturbative checks and new calculations.

Contribution

It formulates a precise integrability-based method for non-planar correlation functions, including stratification and multi-particle mirror contributions, advancing the computational toolkit.

Findings

Formulated a stratification-based approach for non-planar corrections.

Computed previously unknown one-loop multi-particle mirror contributions.

Performed perturbative checks validating the proposed method.

Abstract

In a previous work, we proposed an integrability setup for computing non-planar corrections to correlation functions in $\mathcal{N}=4$ super Yang-Mills theory at any value of the coupling constant. The procedure consists of drawing all possible tree-level graphs on a Riemann surface of given genus, completing each graph to a triangulation, inserting a hexagon form factor into each face, and summing over a complete set of states on each edge of the triangulation. The summation over graphs can be interpreted as a quantization of the string moduli space integration. The quantization requires a careful treatment of the moduli space boundaries, which is realized by subtracting degenerate Riemann surfaces; this procedure is called stratification. In this work, we precisely formulate our proposal and perform several perturbative checks. These checks require hitherto unknown multi-particle mirror contributions at one loop, which we also compute.