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Modular properties of massive scalar partition functions

Authors :
Ankit Aggarwal
Glenn Barnich
Source :
Journal of High Energy Physics, Vol 2024, Iss 9, Pp 1-32 (2024)
Publication Year :
2024
Publisher :
SpringerOpen, 2024.

Abstract

Abstract We compute the exact thermal partition functions of a massive scalar field on flat spacetime backgrounds of the form ℝ d−q × 𝕋 q+1 and show that they possess an SL(q + 1, ℤ) symmetry. Non-trivial relations between equivalent expressions for the result are obtained by doing the computation using functional, canonical and worldline methods. For q = 1, the results exhibit modular symmetry and may be expressed in terms of massive Maass-Jacobi forms. In the complex case with chemical potential for U(1) charge turned on, the usual discussion of relativistic Bose-Einstein condensation is modified by the presence of the small dimensions.

Details

Language :
English
ISSN :
10298479
Volume :
2024
Issue :
9
Database :
Directory of Open Access Journals
Journal :
Journal of High Energy Physics
Publication Type :
Academic Journal
Accession number :
edsdoj.8e5b1d7fc6774b66a6e6b123c00a3452
Document Type :
article
Full Text :
https://doi.org/10.1007/JHEP09(2024)127