Edge Modes on Stringy Horizons

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.

💡 Research Summary

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The paper investigates the contribution of horizon‑localized “edge modes” to the Euclidean one‑loop partition function of quantum fields of arbitrary mass and spin in the static patch of de Sitter (dS) space, and then extends the analysis to string theory near a Minkowski‑Rindler horizon.

First, the authors review the known split of the dS Euclidean partition function into a bulk part and an edge part. For a field of mass m and spin s the bulk contribution is encoded in a Harish‑Chandra character χ_bulk(u)=tr G e^{-iuH} of the unitary infinite‑dimensional representation