$\mathcal{N}=1$ Super Topological Recursion

TL;DR

This paper develops a supersymmetric extension of topological recursion using super spectral curves and super Airy structures, enabling the computation of correlation functions in 2D supergravity.

Contribution

It introduces $ abla=1$ super loop equations and provides two equivalent recursive solutions, extending topological recursion to supersymmetric settings.

Findings

Formulation of $ abla=1$ super loop equations.

Two equivalent recursive methods for solutions.

Application to 2D supergravity correlation functions.

Abstract

We introduce the notion of $\mathcal{N}=1$ abstract super loop equations, and provide two equivalent ways of solving them. The first approach is a recursive formalism that can be thought of as a supersymmetric generalization of the Eynard-Orantin topological recursion, based on the geometry of a local super spectral curve. The second approach is based on the framework of super Airy structures. The resulting recursive formalism can be applied to compute correlation functions for a variety of examples related to 2d supergarvity.