# Octagons I: Combinatorics and Non-Planar Resummations

## TL;DR

This paper develops a resummation method for correlators of half-BPS operators in N=4 super Yang-Mills theory at large charge, expressing the results through a novel octagon function and dual matrix models.

## Contribution

It introduces a new large-charge limit resummation technique for correlators using an octagon function and dual matrix model representations, revealing non-trivial dependence on coupling and spacetime.

## Key findings

- Correlators are expressed as polynomials in the octagon at each genus.
- The large-charge limit simplifies the correlators to a function of two variables.
- Dual matrix models with zero colors describe the correlators in this limit.

## Abstract

We explain how the 't Hooft expansion of correlators of half-BPS operators can be resummed in a large-charge limit in N=4 super Yang-Mills theory. The full correlator in the limit is given by a non-trivial function of two variables: One variable is the charge of the BPS operators divided by the square root of the number Nc of colors; the other variable is the octagon that contains all the 't Hooft coupling and spacetime dependence. At each genus g in the large Nc expansion, this function is a polynomial of degree 2g+2 in the octagon. We find several dual matrix model representations of the correlators in the large-charge limit. Amusingly, the number of colors in these matrix models is formally taken to zero in the relevant limit.