Edge Modes on Stringy Horizons

TL;DR

The paper develops a horizon-edge viewpoint for quantum fields in curved spacetime and extends it to the full string theory tower. By regulating near-horizon physics with a large-radius $dS_3$ and summing over the entire string spectrum, the authors derive a modular-invariant, UV-finite edge partition function $Z_{\text{edge}}$ obtained from a Kronecker limit-form regularization of Eisenstein series, and express both bulk and edge sectors in terms of Harish-Chandra characters. This yields a concrete, state-counting interpretation for edge modes as two-dimensional degrees of freedom with modular properties, and identifies the edge contribution with the center of the horizon algebra, with potential connections to entanglement entropy and holography. The results provide a controlled, string-theoretic realization of horizon edge physics that is free of UV divergences and captures the full tower of string states, highlighting the role of modular invariance in regulating horizon physics.

Abstract

For a quantum field of arbitrary mass and spin in the static patch of de Sitter spacetime, the Euclidean partition function receives contributions from edge modes localized on the horizon, expressible in terms of the Harish-Chandra character of the de Sitter group. Considering the flat limit and summing over all string fields, we obtain the partition function of edge modes in string theory near the Minkowski-Rindler horizon. Application of the Kronecker limit formula naturally yields a modular invariant one-loop partition function. The resulting expression generalizes the edge contribution of a massive vector boson in a spontaneously broken gauge theory to the infinite tower in string theory. It is naturally ultraviolet finite and amenable to a state-counting interpretation.