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arXiv · 1412.7463

Comments on the Casimir energy in supersymmetric field theories

Jakob Lorenzen·Dario Martelli
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Abstract

We 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 $S^1\times S^3$, we recover the supersymmetric Casimir energy. 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.

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Jakob Lorenzen, Dario Martelli. 2015-07-08. Comments on the Casimir energy in supersymmetric field theories. https://doi.org/10.1007/jhep07(2015)001

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