Insertion of vertex operators using BV formalism

TL;DR

This paper develops a comprehensive BV formalism framework for inserting vertex operators on the string worldsheet, enabling a global and systematic approach to gauge symmetry deformations and their restoration.

Contribution

It introduces a general, globally defined construction for vertex operator insertions in BV formalism, extending previous local conjectures and linking gauge symmetry enhancement to BV effective actions.

Findings

Provides a global construction on the moduli space

Derives an integral formula for deformation of contraction operators

Connects gauge symmetry enhancement with BV effective action

Abstract

We develop a general framework for the insertion of vertex operator on the string worldsheet, in BV formalism. Such insertions correspond to deformations of the Master Action which breaks the gauge symmetry to a subgroup, and then restoring the full gauge symmetry by integrating over a cycle in the space of Lagrangian submanifolds. We provide the general construction, global on the moduli space, which was previously conjectured in a form local on the worldsheet. We explain how the enhancement of the gauge symmetry in equivariant BV formalism can be seen as an application of the general idea of BV effective action. We derive an integral formula for the deformation of the contraction operator due to the vertex insertion.