I will discuss the M2-brane partition function for large class of asymptotically locally AdS_4 x S^7 spacetimes. I will show how supersymmetry localises the M2-brane position to a fixed point of an R-symmetry Killing vector. I will then discuss the one-loop partition function of instantonic M2-branes and show that it is assembled out of building blocks familiar to 3D supersymmetric quantum field theories. I will close out with a discussion of possible one-loop exactness of the answer and what it means for supersymmetric localisation of the M2-brane partition function.

I will discuss a few examples of holographic dual pairs that arise in string theory for quantum theories that are not conformal. In particular, we will focus on Euclidean supersymmetric gauge theories on spheres and compute observables using supergravity and string theory on one side of the duality and supersymmetric localization on the other. This two-pronged approach allows us to study perturbative and non-perturbative corrections to the leading-order holographic result.

I will discuss a few examples of holographic dual pairs that arise in string theory for quantum theories that are not conformal. In particular, we will focus on Euclidean supersymmetric gauge theories on spheres and compute observables using supergravity and string theory on one side of the duality and supersymmetric localization on the other. This two-pronged approach allows us to study perturbative and non-perturbative corrections to the leading-order holographic result.