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arXiv · 1805.05646

Character Integral Representation of Zeta function in AdS$_{d+1}$: I. Derivation of the general formula

Thomas Basile·Euihun Joung·Shailesh Lal·Wenliang Li
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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 AdS$_4$ and AdS$_5$ 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 AdS$_{d+1}$ with $d=2,3,4,5,6$.

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Thomas Basile, Euihun Joung, Shailesh Lal, Wenliang Li. 2018-08-22. Character Integral Representation of Zeta function in AdS$_{d+1}$: I. Derivation of the general formula. https://doi.org/10.1007/jhep10(2018)091

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