B-field transformations of Poisson groupoids

TL;DR

This paper explores how B-field transformations, represented by multiplicative closed 2-forms, act on Poisson groupoids and their Dirac structures, extending existing results and analyzing infinitesimal symmetries.

Contribution

It extends the theory of B-field transformations to Poisson groupoids using multiplicative Dirac structures and describes their infinitesimal symmetries.

Findings

Extended gauge transformation results for symplectic/Poisson groupoids.

Unified multiplicative Dirac structures framework.

Characterized B-field symmetries at the infinitesimal level.

Abstract

In this work we study B-field transformations of multiplicative Poisson bivectors on a Lie groupoid G. We are concerned with B-fields given by multiplicative closed 2-forms on G. We view Poisson groupoids and their B-field symmetries as special instances of multiplicative Dirac structures. These are geometric structures that unify both multiplicative Poisson bivectors and multiplicative closed 2-forms. This allows us to extend results of Bursztyn and Radko on gauge transformations of symplectic/Poisson groupoids. We also describe B-field symmetries of Poisson groupoids at the infinitesimal level.