Davide Cassani

Localization on Hopf surfaces

A bstractWe discuss localization of the path integral for supersymmetric gauge theories with an R-symmetry on Hermitian four-manifolds. After presenting the localization locus equations for the general case, we focus on backgrounds with S1 × S3 topology, admitting two supercharges of opposite R-charge. These are Hopf surfaces, with two complex structure moduli p, q. We compute the localized partition function on such Hopf surfaces, allowing for a very large class of Hermitian metrics, and prove that this is proportional to the supersymmetric index with fugacities p, q. Using zeta function regularisation, we determine the exact proportionality factor, finding that it depends only on p, q, and on the anomaly coefficients a, c of the field theory. This may be interpreted as a supersymmetric Casimir energy, and provides the leading order contribution to the partition function in a large N expansion.

The Casimir Energy in Curved Space and its Supersymmetric Counterpart

A bstractWe study d-dimensional Conformal Field Theories (CFTs) on the cylinder, Sd−1×ℝ

All homogeneous N = 2 M-theory truncations with supersymmetric AdS4 vacua

{S}^{d-1}\times \mathrm{\mathbb{R}}

The gravity dual of supersymmetric gauge theories on a squashed S 1 S 3

, and its deformations. In d = 2 the Casimir energy (i.e. the vacuum energy) is universal and is related to the central charge c. In d = 4 the vacuum energy depends on the regularization scheme and has no intrinsic value. We show that this property extends to infinitesimally deformed cylinders and support this conclusion with a holographic check. However, for N=1

Exceptional generalised geometry for massive IIA and consistent reductions

\mathcal{N}=1

The holographic supersymmetric Casimir energy

supersymmetric CFTs, a natural analog of the Casimir energy turns out to be scheme independent and thus intrinsic. We give two proofs of this result. We compute the Casimir energy for such theories by reducing to a problem in supersymmetric quantum mechanics. For the round cylinder the vacuum energy is proportional to a + 3c. We also compute the dependence of the Casimir energy on the squashing parameter of the cylinder. Finally, we revisit the problem of supersymmetric regularization of the path integral on Hopf surfaces.