Superconformal topological recursion

TL;DR

This paper develops a supersymmetric extension of topological recursion, linking algebraic structures of super Virasoro modules with geometric super Riemann surface analysis, advancing understanding of supergeometry and deformation theory.

Contribution

It introduces superconformal topological recursion, connecting algebraic super Virasoro modules with geometric super Riemann surfaces, and explores deformation and recursion involving odd parameters.

Findings

Odd holomorphic one-forms relate to Clifford algebra zero modes.

Provides a recursive framework for super Riemann surface deformations.

Extends topological recursion to supersymmetric and supergeometric contexts.

Abstract

We investigate a supersymmetric generalisation of topological recursion from two perspectives: algebraic and geometric. The algebraic side concerns a recursive structure encoded in modules of a super Virasoro algebra, and the geometric counterpart is what we call superconformal topological recursion defined on a super Riemann surface. Superconformal topological recursion indicates that odd holomorphic one-forms on a super Riemann surface are related to zero modes of copies of the Clifford algebras, and it also provides a tool to study deformation of non-split super Riemann surfaces, e.g. certain families of super Riemann surfaces carrying odd parameters. On a super Riemann surface over a non-reduced base, the formalism is recursive not only in terms of pants-decomposition but also in terms of odd parameters in a suitable sense.