An Introduction to Generalised Dualities and their Applications to Holography and Integrability

Abstract

These pedagogical lectures given at the Corfu Summer Institute 2018 review two generalised notions of T-duality, non-Abelian T-duality and Poisson-Lie duality, and their applications. We explain how each of these has seen recent application in the context of holography. Non-Abelian T-duality has been used to construct new holographic dual geometries. Poisson-Lie duality has been used to construct new integrable string sigma-models including the $\eta$- and $\lambda$-deformations of the $Ad{S}_5\times S^5$ superstring thought to encode quantum group deformations of holography. We also comment on the doubled worldsheet description that makes such dualities manifest.

arXiv commentProceedings to Corfu Summer Institute 2018 "School and Workshops on Elementary Particle Physics and Gravity", Review article/Introductory lectures, 61pages