Open intersection numbers and free fields

TL;DR

This paper expresses the Virasoro and W-constraints for the Kontsevich-Penner model using free bosonic fields with twisted boundary conditions, linking to spectral curves and topological recursion.

Contribution

It introduces a novel free field representation of the constraints, enhancing the understanding of open intersection numbers and their relation to conformal field theory.

Findings

Constraints described via free bosonic fields with twisted boundary conditions

Connection established between spectral curve description and algebraic constraints

Provides a new tool for topological recursion and Givental decomposition

Abstract

A complete set of the Virasoro and W-constraints for the Kontsevich-Penner model, which conjecturally describes intersections on moduli spaces of open curves, was derived in our previous work. Here we show that these constraints can be described in terms of free bosonic fields with twisted boundary conditions, which gives a modification of the well-known construction of the $W^{(3)}$ algebra in conformal field theory. This description is natural from the point of view of the spectral curve description, and should serve as a new important ingredient of the topological recursion/Givental decomposition.