Abstract
We relate the heat kernel and quasinormal mode methods of computing the 1-loop partition function of arbitrary spin fields on a rotating (Euclidean) BTZ background using the Selberg zeta function associated with ℍ3/ℤ, extending (arXiv:1811.08433) [1]. Previously, Perry and Williams [2] showed for a scalar field that the zeros of the Selberg zeta function coincide with the poles of the associated scattering operator upon a relabeling of integers. We extend the integer relabeling to the case of general spin, and discuss its relationship to the removal of non-square-integrable Euclidean zero modes.
Highlights
AdS3 spacetimes, namely the Banados, Teitelboim and Zanelli (BTZ) black hole [10] and thermal AdS3
We relate the heat kernel and quasinormal mode methods of computing the 1-loop partition function of arbitrary spin fields on a rotating (Euclidean) BTZ background using the Selberg zeta function associated with H3/Z, extending [1]
Perry and Williams [2] showed for a scalar field that the zeros of the Selberg zeta function coincide with the poles of the associated scattering operator upon a relabeling of integers
Summary
The background M = H3/Γ is an example of a homogeneous space M = G/H [13] Are such spacetimes of physical interest, but their high degree of symmetry allows one to use group theoretic techniques to write down the eigenfunctions ψn(s,a) of the spin-s Laplacian ∇2(s) in terms of matrix elements of representations of the symmetry group of M. The first task is to construct the heat kernel of a free field of spin-s on Euclidean AdS3. Upon integrating over the fundamental domain of H3/Z, the integrated heat kernel for thermal AdS3 for fields of spin s is [13]. In the context of AdS3/CFT2, ∆s represents the conformal dimension of the CFT2 operator dual to a spin-s field propagating on AdS3
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