Strings, Branes, Schwarzian Action and Maximal Chaos

TL;DR

This paper demonstrates that probe string and brane degrees of freedom in holographic gauge theories exhibit maximal chaos, characterized by an emergent Schwarzian action and intrinsic horizons, with explicit calculations supporting these phenomena.

Contribution

It provides the first explicit evidence linking the Schwarzian effective action to maximal chaos in probe branes and strings within holographic models.

Findings

Maximal chaos occurs for probe string and brane degrees of freedom.

An emergent Schwarzian action governs the soft sector in these systems.

Explicit four-point correlator calculations confirm maximal chaos.

Abstract

In this article, we present explicit evidence that maximal chaos occurs for a generic, probe quark-like defect degrees of freedom, in a strongly coupled large $N_c$ gauge theory. In holography, this corresponds to the dynamics of open string degrees of freedom, in the background of a closed string geometry. In this context, we explicitly show that a Schwarzian effective action for the soft sector emerges and couples with other modes, in the infra-red. This is manifest on an open string worldsheet, as well as a D$1$-brane world-volume, embedded in AdS$_3$. The corresponding maximal chaos is governed by an intrinsic defect D-brane horizon, and an intrinsic non-linear description of the brane or the string. We also present explicit evidence of maximal chaos away from extremality on a D-brane horizon, by computing a four-point out-of-time order correlator of spin-one operators. This further suggests that a similar description of the soft sector physics of open string degrees of freedom may exist in general.