Non-abelian T-duality, generalised geometry and holography

TL;DR

This paper reviews recent advances connecting non-abelian T-duality with generalised geometry, demonstrating how it transforms supersymmetric solutions and aids in holographic model building, including adding flavor via smeared sources.

Contribution

It establishes the transformation rules of pure spinors under non-abelian T-duality and explores their implications for holography and supersymmetric solutions.

Findings

SU(3) structures map to SU(2) structures under duality

Transformation rules for pure spinors are derived

Guidance on adding flavor through smeared sources in T-duals

Abstract

Recent progress which relates non-abelian T-duality of $\mathcal{N}=1$ SuGra solutions to the powerful techniques of Generalised geometry is reviewed. It is shown that SU(3) structure solutions are mapped to SU(2) structures and the transformation rule of the corresponding pure spinors is presented. This constitutes an important step on the road towards the utility of the duality within holography, showing for example, how smeared sources must transform and so how to add flavour to the T-duals.