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  Modular forms in the spectral action of Bianchi IX gravitational instantons

Fan, W., Fathizadeh, F., & Marcolli, M. (2019). Modular forms in the spectral action of Bianchi IX gravitational instantons. Journal of High Energy Physics, 2019(1): 234, pp. 1-37. doi:10.1007/JHEP01(2019)234.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0003-0545-A Version Permalink: http://hdl.handle.net/21.11116/0000-0003-9A33-6
Genre: Journal Article

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Fan, W, Author
Fathizadeh, F1, 2, Author              
Marcolli, M, Author
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1Department Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497798              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: We prove a modularity property for the heat kernel and the Seeley-deWitt coefficients of the heat kernel expansion for the Dirac-Laplacian on the Bianchi IX gravitational instantons. We prove, via an isospectrality result for the Dirac operators, that each term in the expansion is a vector-valued modular form, with an associated ordinary (meromorphic) modular form of weight 2. We discuss explicit examples related to well known modular forms. Our results show the existence of arithmetic structures in Euclidean gravity models based on the spectral action functional.

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 Dates: 2019-01
 Publication Status: Published online
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 Identifiers: DOI: 10.1007/JHEP01(2019)234
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Title: Journal of High Energy Physics
Source Genre: Journal
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Publ. Info: Bologna, Italy : Società italiana di fisica
Pages: - Volume / Issue: 2019 (1) Sequence Number: 234 Start / End Page: 1 - 37 Identifier: ISSN: 1126-6708
CoNE: https://pure.mpg.de/cone/journals/resource/111021927548002_1