# Soft Hair as a Soft Wig

## TL;DR

This paper demonstrates that in asymptotically flat spacetime, soft gauge modes decouple from hard dynamics, implying large gauge symmetries do not resolve the black hole information paradox, with quantum soft decoupling confirmed.

## Contribution

It introduces a canonical transformation that decouples soft variables from hard dynamics in gravity and electromagnetism, clarifying their physical role and implications.

## Key findings

- Soft variables decouple from hard dynamics at the classical level.
- Large gauge symmetries do not influence the black hole information paradox.
- Quantum soft decoupling is explicitly demonstrated.

## Abstract

We consider large gauge transformations of gravity and electromagnetism in D=4 asymptotically flat spacetime. Already at the classical level, we identify a canonical transformation that decouples the soft variables from the hard dynamics. We find that only the soft dynamics is constrained by BMS or large U(1) charge conservation. Physically this corresponds to the fact that sufficiently long-wavelength photons or gravitons that are added to the in-state will simply pass through the interaction region; they scatter trivially in their own sector. This implies in particular that the large gauge symmetries bear no relevance to the black hole information paradox. We also present the quantum version of soft decoupling. As a consistency check, we show that the apparent mixing of soft and hard modes in the original variables arises entirely from the long range field of the hard charges, which is fixed by gauge invariance and so contains no additional information.