Theory HEP Seminar

Horizon Scattering, Partition Functions, and Edge Modes

Y. T. Albert Law

Harvard University

When computing the ideal gas thermal canonical partition function for quantum fields outside a (black hole or de Sitter) horizon, one encounters the infinite single-particle density of states (DOS) due to the continuous nature of the normal mode spectrum. In the first part of the talk, I will explain how to make sense of the computation by viewing the Lorentzian field equation as an effective 1D scattering problem: the scattering phases encode non-trivial information about the DOS and can be extracted by ``renormalizing" the DOS with respect to a reference. This defines a renormalized free energy up to a choice of reference free energy. Interestingly, we discover that the 1-loop Euclidean path integral, as computed by the Denef-Hartnoll-Sachdev (DHS) formula, fixes the reference free energy to be that on a Rindler-like region. In the second part of the talk, I will explain how extending the DHS argument to spinning fields allows us to reveal a manifestly covariant bulk-edge split for their Euclidean partition functions: the bulk part captures the renormalized thermal free energy described above; the edge part is related to QNMs that fail to analytically continue to a subset of Euclidean modes with enhanced fall-offs near the origin.