Document Type : Regular article

Author

• Leonard Susskind

LITP and Department of Physics, Stanford University, Stanford, CA 94305-4060, USA; Google, Mountain View, CA, USA

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 1.3. 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 [1] say yes; time-reversal is a gauge symmetry. Witten [2]  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