On a conjectural solution to open KdV and Virasoro

TL;DR

This paper proposes a recursive formula for the full partition function of open and closed Riemann surface integrals, based on a conjecture linking it to open KdV and Virasoro equations, advancing understanding in mathematical physics.

Contribution

It introduces a recursive formula for the partition function assuming the conjecture that it satisfies open KdV and Virasoro equations, providing a new computational approach.

Findings

Recursive formula for the partition function Z

Supports the conjecture relating Z to open KdV and Virasoro equations

Provides a foundation for further mathematical physics research

Abstract

In this note, we present a recursive formula for the full partition function Z of descendent integrals over moduli spaces of open and closed Riemann surfaces, assuming the conjecture recently proposed by Pandharipande, Solomon and Tessler that Z satisfies the open KdV and Virasoro equations.