Higher spin partition functions via the quasinormal mode method in de Sitter quantum gravity

Abstract

In this note we compute the 1-loop partition function of spin-$s$ fields on Euclidean de Sitter space $S^{2n+1}$ using the quasinormal mode method. Instead of computing the quasinormal mode frequencies from scratch, we use the analytic continuation prescription $L_{\text{AdS}}\to i{L}_{\text{dS}}$, appearing in the dS/CFT correspondence, and Wick rotate the normal mode frequencies of fields on thermal ${\text{AdS}}_{2n+1}$ into the quasinormal mode frequencies of fields on de Sitter space. We compare the quasinormal mode and heat kernel methods of calculating 1-loop determinants, finding exact agreement, and furthermore explicitly relate these methods via a sum over the conformal dimension. We discuss how the Wick rotation of normal modes on thermal ${\text{AdS}}_{2n+1}$ can be generalized to calculating 1-loop partition functions on the thermal spherical quotients $S^{2n+1}/{\mathbb{Z}}_p$. We further show that the quasinormal mode frequencies encode the group theoretic structure of the spherical spacetimes in question, analogous to the recent analysis made for thermal AdS in (1910.07607) and (1910.11913).

arXiv comment18 pages, clarifications added, scipost formatting

References in corpus (29)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• The dS/CFT Correspondence
• Quantum Gravity In De Sitter Space
• On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces
• One-loop Partition Functions of 3D Gravity
• A Black Hole Farey Tail
• Holographic entanglement beyond classical gravity
• De Sitter Musings
• Quantum oscillations and black hole ringing
• De Sitter Holography and Entanglement Entropy
• Black hole determinants and quasinormal modes
• Quasinormal modes of D-dimensional de Sitter spacetime
• The Heat Kernel on AdS_3 and its Applications
• A de Sitter Farey Tail
• The Heat Kernel on $AdS$
• Effective action in spherical domains
• Tweaking one-loop determinants in AdS${}_3$
• Dirac quasinormal modes of D-dimensional de Sitter spacetime
• Higher spin quasinormal modes and one-loop determinants in the BTZ black hole
• Quantum Topologically Massive Gravity in de Sitter Space
• Higher spin fermions in the BTZ black hole
• Connecting quasinormal modes and heat kernels in 1-loop determinants
• BTZ one-loop determinants via the Selberg zeta function for general spin
• Massive sphere determinants
• Functional determinants, generalized BTZ geometries and Selberg zeta function
• Normal modes in thermal AdS via the Selberg zeta function
• The spectrum on $p$-forms of a lens space
• Functional determinants on spheres and sectors
• Lens space determinants

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