Is Time Reversal in de Sitter Space a Spontaneously Broken Gauge Symmetry?

TL;DR

This paper explores whether time-reversal symmetry in de Sitter space is a gauge symmetry that is spontaneously broken, proposing a novel perspective that reconciles differing views and introduces a specific observable signature.

Contribution

It argues that time-reversal in de Sitter space is a gauge symmetry that is spontaneously broken, providing a new conceptual framework and identifying a holonomy as a key signature.

Findings

Time-reversal symmetry can be a hidden gauge symmetry in de Sitter space.

Spontaneous symmetry breaking of time-reversal leads to observable holonomies.

A specific 'smoking gun' holonomy flips clocks, indicating broken symmetry.

Abstract

I'll begin with some well-deserved acknowledgements: I am grateful to Daniel Harlow for discussions of time-reversal holonomies. I have also benefited from a long ongoing correspondence with Edward Witten, but frankly in both cases I can't tell whether they agree with me or not. I have often been accused of imprecision, especially toward the later parts of a paper, where I expect that my readers have ``caught on." That does eventually happen -- the readers catching on and I thank them -- but I'm now almost 86 and I can't wait. So I've tried to maintain a level of conceptual if not mathematical rigor throughout. Mathematical rigor(mortis) can sometimes be the enemy of conceptual clarity. I thank my friend Richard Feynman for reminding me of that lesson. Finally I thank the chatbot who gave me the definition of scaffold in section \ref{Scaff}. It was better than anything I was able to do. Symmetries of a Holographic theory; whether continuous or discrete, local or global, are gauge symmetries of the bulk. This includes discrete space-time symmetries such as C and P. But time-reversal is sufficiently different from other symmetries that we may question the standard wisdom and ask whether symmetries involving T should be gauged in the bulk. Harlow and Numasawa \cite{Harlow:2023hjb} say yes; time-reversal is a gauge symmetry. Witten \cite{Witten:2025ayw} says no: time reversal is different and does not manifest as a gauge symmetry of the bulk. My view is -- yes -- but with a twist: Time-reversal is indeed a gauge symmetry; but it is hidden by spontaneous symmetry breaking. In this paper I will review the case for spontaneous symmetry breaking of time-reversal and explain the ``smoking gun" -- a closed curve and a holonomy which flips forward-going clocks to backward going clocks, and vice versa.