The exceptional holography of the M5-brane

The characterisation of the physics of the M5-brane remains an important open problem in string theory. While the superconformal field theory that resides on a planar M5-brane in flat space is poorly understood, other configurations involving M5-branes wrapped on certain manifolds have well-known superconformal field theory descriptions, including N=2 class S field theories. In this talk, I will use new methods based on exceptional generalised geometry to describe the gravity duals of class S field theories, compute a universal sector of their light-operator spectrum, and provide, for the first time, a holographic match of their superconformal index.