Document Type : Regular article

Author

• Leonard Susskind

Stanford Institute for Theoretical Physics and Department of Physics

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{GS}. 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.

Keywords

• Holography
• Gauge Symmetry
• Holonomy

Main Subjects

• Physics