Abstract
AbstractWe study the Casimir energy of four-dimensional supersymmetric gauge theories in the context of the rigid limit of new minimal supergravity. Firstly, revisiting the computation of the localized partition function on S1 × S3, we recover the supersymmetric Casimir energy from its path integral definition. Secondly, we consider the same theories in the Hamiltonian formalism on \( \mathbb{R}\times {S}^3 \), focussing on the free limit and including a one- parameter family of background gauge fields along \( \mathbb{R} \). We compute the vacuum expectation value of the canonical Hamiltonian using zeta function regularization, and show that this interpolates between the supersymmetric Casimir energy and the ordinary Casimir energy of a supersymmetric free field theory.
Highlights
Background geometryWe begin with the background in Euclidean signature, discussing the differences in Lorentzian signature later
We study the Casimir energy of four-dimensional supersymmetric gauge theories in the context of the rigid limit of new minimal supergravity
We find that using our regularization, the Casimir energy of a supersymmetric gauge theory with Nv vector multiplets and Nχ chiral multiplets with R-charges rI is given by the following expression q4 − 2q3 + q + 1
Summary
We present the background geometry, that we view as a solution to the rigid limit of new supergravity and introduce the relevant supersymmetric Lagrangians. We follow verbatim the notation of [2], to which we refer for more details
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