Sasaki-Einstein Geometry, GK Geometry and the AdS/CFT correspondence

Abstract

We review various aspects of Sasaki-Einstein and GK geometry, emphasising their similarities, interconnections and significance for the AdS/CFT correspondence. In particular, we highlight the key role that physical considerations have played in formulating geometric extremization principles, which have been instrumental in both understanding the geometry and identifying the corresponding dual field theories.

arXiv comment23 pages. Invited contribution to the book "Half a Century of Supergravity'', editors A. Ceresole and G. Dall'Agata. Minor changes, final version