Doubled aspects of generalised dualities and integrable deformations

TL;DR

This paper develops a framework within Double Field Theory to describe Poisson-Lie T-dualisable sigma-models and integrable deformations, providing new criteria for background fields and a tool for analyzing Poisson-Lie symmetric spacetimes.

Contribution

It introduces an elegant target space description of ${ m extbf{E}}$-models using generalized frame fields in Double Field Theory, extending conditions for type II backgrounds to be Poisson-Lie T-dualisable.

Findings

Derived simple criteria for R/R fields and dilaton in type II backgrounds.

Provided algebraic field equations for Poisson-Lie symmetric spacetimes.

Established a systematic approach for studying integrable deformations and dualities.

Abstract

The worldsheet theories that describe Poisson-Lie T-dualisable $\sigma$-models on group manifolds as well as integrable $\eta$, $\lambda$ and $\beta$-deformations provide examples of ${\cal E}$-models. Here we show how such ${\cal E}$-models can be given an elegant target space description within Double Field Theory by specifying explicitly generalised frame fields forming an algebra under the generalised Lie derivative. With this framework we can extract simple criteria for the R/R fields and the dilaton that extend the ${\cal E}$-model conditions to type II backgrounds. In particular this gives conditions for a type II background to be Poisson-Lie T-dualisable. Our approach gives rise to algebraic field equations for Poisson-Lie symmetric spacetimes and provides an effective tool for their study.