Partition Functions with spin in AdS_2 via Quasinormal Mode Methods

Abstract

We extend the results of arXiv:1401.7016, computing one loop partition functions for massive fields with spin half in AdS_2 using the quasinormal mode method proposed by Denef, Hartnoll, and Sachdev in arXiv:0908.2657. We find the finite representations of SO(2,1) for spin zero and spin half, consisting of a highest weight state |h\rangle and descendants with non-unitary values of h. These finite representations capture the poles and zeroes of the one loop determinants. Together with the asymptotic behavior of the partition functions (which can be easily computed using a large mass heat kernel expansion), these are sufficient to determine the full answer for the one loop determinants. We also discuss extensions to higher dimensional AdS_{2n} and higher spins.

18 pages + appendix; V2 has an extended section 5, following a suggestion by the referee

References in corpus (9)

• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• Real-time response in AdS/CFT with application to spinors
• Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
• Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT
• Logarithmic Corrections to $N\ge 2$ Black Hole Entropy
• Fermion-Scalar Conformal Blocks
• Quantum Corrections to Supergravity on AdS${}_2\times S^2$
• Holographic formula for the determinant of the scattering operator in thermal AdS
• One loop partition function from normal modes for $\mathcal{N}=1$ supergravity in AdS${}_3$

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• Siegel Modular Forms and Black Hole Entropy
• Computing black hole partition functions from quasinormal modes
• Black hole one-loop determinants in the large dimension limit