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

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 $AdS_5\times S^5$ superstring thought to encode quantum group deformations of holography. We also comment on the doubled worldsheet description that makes such dualities manifest.