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 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.
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Lorenzen, J., Martelli, D. Comments on the Casimir energy in supersymmetric field theories. J. High Energ. Phys. 2015, 1 (2015). https://doi.org/10.1007/JHEP07(2015)001
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DOI: https://doi.org/10.1007/JHEP07(2015)001