Compatibility of Poisson--Lie transformations with symmetries of Generalized Supergravity Equations

TL;DR

This paper explores how Poisson--Lie transformations interact with symmetries in Generalized Supergravity Equations, identifying conditions for compatible dilaton and vector field configurations.

Contribution

It characterizes the admissible dilaton and vector field configurations compatible with Poisson--Lie transformations under supergravity symmetries.

Findings

Identified conditions for admissible dilatons and vector fields

Presented examples illustrating compatibility constraints

Clarified the role of symmetries in supergravity transformations

Abstract

We investigate two types of transformations that keep NS-NS Generalized Supergravity Equations satisfied : $\chi$-symmetry that shifts dilaton and gauge transformations that change both dilaton and vector field $J$. Due to these symmetries there is a large set of dilatons and vector fields $J$ that (for a fixed metric and B-field) satisfy Generalized Supergravity Equations but only some of them can be be used as input for Poisson--Lie transformations. Conditions that define the admissible dilatons are given and examples are presented.