TBA

I will discuss how to construct rigid supersymmetric gauge theories on Riemannian five-manifolds following a holographic approach. This approach realises the five-manifold as the conformal boundary of a six-dimensional bulk supergravity solution and leads to a systematic classification of five-dimensional supersymmetric backgrounds with gravity duals. The background metric is furnished with a conformal Killing vector, which generates a transversely holomorphic foliation with a transverse Hermitian structure. Finally, I’ll also construct supersymmetric Lagrangians for gauge theories coupled to arbitrary matter on such backgrounds.

I will discuss how to construct rigid supersymmetric gauge theories on Riemannian five-manifolds following a holographic approach. This approach realises the five-manifold as the conformal boundary of a six-dimensional bulk supergravity solution and leads to a systematic classification of five-dimensional supersymmetric backgrounds with gravity duals. The background metric is furnished with a conformal Killing vector, which generates a transversely holomorphic foliation with a transverse Hermitian structure. Finally, I’ll also construct supersymmetric Lagrangians for gauge theories coupled to arbitrary matter on such backgrounds.

In this talk I will discuss the localisation of supersymmetric gauge theories on Riemannian three-manifolds with the topology of a three-sphere. The three-manifold is always equipped with an almost contact structure and an associated Reeb vector field. The partition function depends only on this vector field and has an explicit expression in terms of the double sine function. In addition, I will discuss the possibility of generalising this work to five dimensions.