Modular properties of massive scalar partition functions
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 u...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2024-09-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP09(2024)127 |
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| Summary: | 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. |
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| ISSN: | 1029-8479 |