Time-reparametrization invariance: from Glasses to toy Black Holes

TL;DR

This paper explores the shared features of glassy dynamics and toy models of quantum gravity, like the SYK model, highlighting their common origin and potential mutual insights.

Contribution

It reveals a deep connection between glassy systems and supersymmetric SYK models, suggesting shared underlying mechanisms and cross-disciplinary benefits.

Findings

Glassy dynamics exhibit time-reparametrization softness.

SYK models show similar reparametrization excitations.

The connection suggests mutual insights between condensed matter and quantum gravity.

Abstract

Glassy dynamics have time-reparametrization `softness': glasses fluctuate, and respond to external perturbations, primarily by changing the pace of their evolution. Remarkably, the same situation also appears in toy models of quantum field theory such as the Sachdev-Ye-Kitaev (SYK) model, where the excitations associated to reparametrizations play the role of an emerging `gravity'. I describe here how these two seemingly unrelated systems share common features, arising from a technically very similar origin. This connection is particularly close between glassy dynamics and supersymmetric variants of the SYK model, which I discuss in some detail. Apart from the curiosity that this correspondence naturally arouses, there is also the hope that developments in each field may be useful for the other.