Abstract
The zeta function of an arbitrary field in (d + 1)-dimensional anti-de Sitter (AdS) spacetime is expressed as an integral transform of the corresponding so(2, d) representation character, thereby extending the results of [arXiv:1603.05387] for AdS4 and AdS5 to arbitrary dimensions. The integration in the variables associated with the so(d) part of the character can be recast into a more explicit form using derivatives. The explicit derivative expressions are presented for AdSd+1 with d = 2, 3, 4, 5, 6.
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Basile, T., Joung, E., Lal, S. et al. Character integral representation of zeta function in AdSd+1. Part I. Derivation of the general formula. J. High Energ. Phys. 2018, 91 (2018). https://doi.org/10.1007/JHEP10(2018)091
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DOI: https://doi.org/10.1007/JHEP10(2018)091