Lorenzo Di Pietro

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

Quantum Electrodynamics in d=3 from the ε Expansion.

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

Scalar multiplet recombination at large N and holography

, 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

On supersymmetry, boundary actions and brane charges

\mathcal{N}=1

Quantum Electrodynamics ind=3from theεExpansion

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.

Cardy formula for 4d SUSY theories and localization

A bstractWe consider supersymmetric theories on a space with compact space-like slices. One can count BPS representations weighted by (−1)F, or, equivalently, study supersymmetric partition functions by compactifying the time direction. A special case of this general construction corresponds to the counting of short representations of the superconformal group. We show that in four-dimensional N=1