Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T -duality

Dieter Lüst,David Osten

doi:10.1007/jhep05(2018)165

Abstract

Based on the construction of Poisson-Lie T -dual σ-models from a common parent action we study a candidate for the non-abelian respectively Poisson-Lie T -duality group. This group generalises the well-known abelian T -duality group O(d, d) and we explore some of its subgroups, namely factorised dualities, B- and β-shifts. The corresponding duality transformed σ-models are constructed and interpreted as generalised (non-geometric) flux backgrounds.We also comment on generalisations of results and techniques known from abelian T -duality. This includes the Lie algebra cohomology interpretation of the corresponding non-geometric flux backgrounds, remarks on a double field theory based on non-abelian T -duality and an application to the investigation of Yang-Baxter deformations. This will show that homogeneously Yang-Baxter deformed σ-models are exactly the non-abelian T -duality β-shifts when applied to principal chiral models.

Highlights

Dualities are a key aspect of quantum field and string theory, as they connect seemingly different theoretical settings and can be very useful tools for approaching otherwise inaccessible problems
After setting up our conventions and reviewing basics of T duality and Lie bialgebras, we revisit the definition [4] of the non-abelian T -duality (NATD) group to a Poisson-Lie σ-model associated to the Lie bialgebra d = g ⊕d g
After setting the stage in introducing Lie bialgebras and Poisson-Lie T -duality, which motivated the duality group of a Poisson-Lie σ-model corresponding to the Lie bialgebra d, we proposed a method to get some insights into this group, which is some subgroup of O(d, d)

Summary

Introduction

Dualities are a key aspect of quantum field and string theory, as they connect seemingly different theoretical settings and can be very useful tools for approaching otherwise inaccessible problems. In its simplest and most rigorous setting the duality maps two toroidal fibre bundles as target spaces to each other. This duality is based on the global abelian isometries of the target spaces, called abelian T -duality, and extends to the quantum theory (for reviews see [1, 2]). The reasoning behind this does work for (U(1))d-isometries of the target space, and for a generic global group isometry, the dual model does not possess this isometry anymore. This is known as non-abelian T -duality [3]

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