Soft Photon Hair on Schwarzschild Horizon from a Wilson Line Perspective

TL;DR

This paper presents a unified quantum field theory framework for constructing soft dressings at spacetime boundaries, revealing how Wilson lines encode soft hair on Schwarzschild black hole horizons, linking to Hawking-Perry-Strominger's soft hair concept.

Contribution

It introduces a Wilson line-based method to construct soft dressings at horizons, providing a quantum perspective on black hole soft hair that unifies boundary dressings across spacetime.

Findings

Wilson lines act as soft dressings at boundaries.

Black holes carry soft hair via horizon Wilson lines.

Framework connects soft hair to quantum field theory.

Abstract

We develop a unified framework for the construction of soft dressings at boundaries of spacetime, such as the null infinity of Minkowski spacetime and the horizon of a Schwarzschild black hole. The construction is based on an old proposal of Mandelstam for quantizing QED and considers matter fields dressed by Wilson lines. Along time-like paths, the Wilson lines puncturing the boundary are the analogs of flat space Faddeev-Kulish dressings. We focus on the Schwarzschild black hole where our framework provides a quantum-field-theoretical perspective of the Hawking-Perry-Strominger viewpoint that black holes carry soft hair, through a study of the Wilson line dressings, localized on the horizon.