The Casimir energy in curved space and its supersymmetric counterpart

By Benjamin Assel, D. Cassani, L. Pietro, Z. Komargodski, Jakob Lorenzen, D. Martelli. Journal of High Energy Physics, 2015

186 citations recorded by the source corpus.

We study d-dimensional Conformal Field Theories (CFTs) on the cylinder, Sd−1×ℝ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {S}^{d-1}\times \mathrm{\mathbb{R}} $$\end{document}, 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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=1 $$\end{document} 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.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/037abf1bf0114eb9577b2f095d8dec3ad4976a65

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Citations in the corpus

N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model (2017, methodology): “21) is the supersymmetric Casimir energy [14, 15].”
Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes (2018, methodology): “ from a regularised sum of eigenvalues of a supersymmetric Hamiltonian, namely imagining that F(! 1;! 2;’) = 1 2 X n 1;n 20 ˚ n 1;n 2 + 1 2 X n 1;n 20 B n 1;n 2 ; (4.97) where, in the notation of [19], ˚n 1;n 2 ; B n 1;n 2 are the eigenvalues of unpaired modes, which upon reduction on S3 are chiral ”
Top down approach to 6D SCFTs (2018, unknown): “reference [164].”