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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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-09-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP09(2024)127 |
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| author | Ankit Aggarwal Glenn Barnich |
| author_facet | Ankit Aggarwal Glenn Barnich |
| author_sort | Ankit Aggarwal |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8e5b1d7fc6774b66a6e6b123c00a3452 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-8e5b1d7fc6774b66a6e6b123c00a34522024-12-08T12:16:13ZengSpringerOpenJournal of High Energy Physics1029-84792024-09-012024913210.1007/JHEP09(2024)127Modular properties of massive scalar partition functionsAnkit Aggarwal0Glenn Barnich1Institute for Theoretical Physics, TU WienPhysique Théorique et Mathématique, Université libre de Bruxelles and International Solvay InstitutesAbstract 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.https://doi.org/10.1007/JHEP09(2024)127Global SymmetriesThermal Field TheoryField Theories in Higher DimensionsScale and Conformal Symmetries |
| spellingShingle | Ankit Aggarwal Glenn Barnich Modular properties of massive scalar partition functions Journal of High Energy Physics Global Symmetries Thermal Field Theory Field Theories in Higher Dimensions Scale and Conformal Symmetries |
| title | Modular properties of massive scalar partition functions |
| title_full | Modular properties of massive scalar partition functions |
| title_fullStr | Modular properties of massive scalar partition functions |
| title_full_unstemmed | Modular properties of massive scalar partition functions |
| title_short | Modular properties of massive scalar partition functions |
| title_sort | modular properties of massive scalar partition functions |
| topic | Global Symmetries Thermal Field Theory Field Theories in Higher Dimensions Scale and Conformal Symmetries |
| url | https://doi.org/10.1007/JHEP09(2024)127 |
| work_keys_str_mv | AT ankitaggarwal modularpropertiesofmassivescalarpartitionfunctions AT glennbarnich modularpropertiesofmassivescalarpartitionfunctions |