Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Horizon Edge Partition Functions in $Λ>0$ Quantum Gravity

Y. T. Albert Law, Varun Lochab

Abstract

We obtain the spectra of codimension-2 horizon "edge" degrees of freedom for gravity and higher-spin gauge fields in de Sitter space and in the static Nariai spacetime, advancing previous Lorentzian and Euclidean analyses of one-loop thermodynamics. The edge spectra exhibit universal shift symmetries, revealing a novel symmetry-breaking structure in one-loop partition functions with positive cosmological constant. For the graviton, these modes admit a geometric interpretation as fluctuations of the cosmic horizon, which also persists in the Nariai case.

Horizon Edge Partition Functions in $Λ>0$ Quantum Gravity

Abstract

We obtain the spectra of codimension-2 horizon "edge" degrees of freedom for gravity and higher-spin gauge fields in de Sitter space and in the static Nariai spacetime, advancing previous Lorentzian and Euclidean analyses of one-loop thermodynamics. The edge spectra exhibit universal shift symmetries, revealing a novel symmetry-breaking structure in one-loop partition functions with positive cosmological constant. For the graviton, these modes admit a geometric interpretation as fluctuations of the cosmic horizon, which also persists in the Nariai case.
Paper Structure (16 sections, 33 equations, 2 figures, 3 tables)

This paper contains 16 sections, 33 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Gravitons on $S^{d+1}$
  3. Branching the sphere
  4. Nonlinear realization of $SO(d+2)$
  5. Geometric fluctuations of the horizon
  6. Symmetric tensor fields on $S^{d+1}$
  7. Gravitons on $S^2\times S^{d-1}$
  8. Shift symmetries and the geometric interpretation
  9. Discussion
  10. Cornering Gravitational Edge Modes
  11. Edge modes as Goldstones?
  12. Revisiting the Gibbons-Hawking prescription
  13. More General Spacetimes
  14. Acknowledgments
  15. Gravitons on $S^{d+1}$
  16. ...and 1 more sections

Figures (2)

  • Figure 1: A round $S^{d+1}$ arises from a $dS_{d+1}$ static patch by Wick-rotating the observer's proper time and imposing periodicity, $t \to -i\tau$ with $\tau \sim \tau + 2\pi\ell_\text{dS}$. This suggests interpreting the $S^{d+1}$ path integral as a thermal trace, analogous to Euclidean methods in quantum field theory at finite temperature. Subtleties may arise, however, at the (Euclidean) horizon or "bolt" Gibbons:1979xm, the codimension-2 fixed point set (yellow dot) of Euclidean time evolution where the thermal cycle degenerates.
  • Figure 2: $Z_{\rm edge}$ of gravity encodes geometric fluctuations of the Euclidean horizon $S^{d-1}\subset S^{d+1}$: transverse bendings $\phi^a$, intrinsic diffeomorphisms $A_\mu$, and normal-bundle twists $\chi$.