Topological Recursion in The Ramond Sector

TL;DR

This paper develops a recursive formalism for super eigenvalue models in the Ramond sector, revealing a new supersymmetric topological recursion that computes correlation functions without poles at irregular ramification points.

Contribution

It introduces a novel recursive approach for super eigenvalue models in the Ramond sector, connecting supersymmetry with topological recursion methods.

Findings

Free energy truncates at quadratic order in Grassmann couplings.

Derived genus-zero algebraic curve with two ramification points.

Correlation functions lack poles at irregular ramification points due to supersymmetric correction.

Abstract

We investigate supereigenvalue models in the Ramond sector and their recursive structure. We prove that the free energy truncates at quadratic order in Grassmann coupling constants, and consider super loop equations of the models with the assumption that the 1/N expansion makes sense. Subject to this assumption, we obtain the associated genus-zero algebraic curve with two ramification points (one regular and the other irregular) and also the supersymmetric partner polynomial equation. Starting with these polynomial equations, we present a recursive formalism that computes all the correlation functions of these models. Somewhat surprisingly, correlation functions obtained from the new recursion formalism have no poles at the irregular ramification point due to a supersymmetric correction -- the new recursion may lead us to a further development of supersymmetric generalizations of the Eynard-Orantin topological recursion.