The Casimir energy in curved space and its supersymmetric counterpart

DOI10.1007/JHEP07(2015)043zbMATH Open1388.81395arXiv1503.05537OpenAlexW1500307940WikidataQ64038285 ScholiaQ64038285MaRDI QIDQ2635578

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Publication date: 31 May 2018

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Abstract: We study $d$-dimensional Conformal Field Theories (CFTs) on the cylinder, $S^{d-1}imesmathbbR$, 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 $mathcalN=1$ 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.

Full work available at URL: https://arxiv.org/abs/1503.05537

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