Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Casimir Energy in Curved Space and its Supersymmetric Counterpart   We study $d$-dimensional Conformal Field Theories (CFTs) on the cylinder,
$S^{d-1}\times \mathbb{R}$, 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
$\mathcal{N}=1$ 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.

15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg