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A generalized Selberg zeta function for flat space cosmologies
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abstract
Flat space cosmologies (FSCs) are time dependent solutions of three-dimensional (3D) gravity with a vanishing cosmological constant. They can be constructed from a discrete quotient of empty 3D flat spacetime and are also called shifted-boost orbifolds. Using this quotient structure, we build a new and generalized Selberg zeta function for FSCs, and show that it is directly related to the scalar 1-loop partition function. We then propose an extension of this formalism applicable to more general quotient manifolds $\mathcal M/\mathbb Z$, based on representation theory of fields propagating on this background. Our prescription constitutes a novel and expedient method for calculating regularized 1-loop determinants, without resorting to the heat kernel. We compute quasinormal modes in the FSC using the zeroes of a Selberg zeta function, and match them to known results.
Forward citations
Cited by 2 Pith papers
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A spool for every quotient: One-loop partition functions in AdS$_3$ gravity
One-loop partition functions of massive spinning fields on any smooth cusp-free hyperbolic 3-manifold are expressed as Wilson spools, sums over free loops of holonomy traces in lowest-weight sl(2,R) representations.
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Scalar fields and 3D Flat Space Cosmologies
A direct bulk derivation of scalar quasi-normal modes in 3D flat space cosmologies is presented, using a hard-wall boundary condition and complex momenta, together with one-loop partition functions computed in simplif...
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