Strings, Branes, Schwarzian Action and Maximal Chaos

TL;DR

The paper provides explicit evidence that maximal chaos can arise for probe defect degrees of freedom in a strongly coupled large-$N_c$ gauge theory by showing that the IR physics of open string degrees of freedom in AdS$_3$ is governed by a Schwarzian action that couples to heavier modes. It derives the Schwarzian action from both string worldsheet and D$1$-brane worldvolume dynamics and computes a four-point OTOC for a spin-1 current on a D3-D5 defect, finding Lyapunov growth saturating the chaos bound with a defect-specific temperature. It also analyzes scrambling times, showing they depend on brane tension and gauge-group data, and generalizes the soft sector to a family of Schwarzian-like actions with constrained chaos, indicating a universal IR-soft sector for open-string defects. The results bridge SYK-type IR physics and open-string holography, suggesting a universal mechanism for maximal chaos in defect CFTs and prompting further exploration of UV–IR connections and semi-holographic descriptions.

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.

Figures (1)

• Figure 1: The $(1+1)$-dimensional geometry, embedded in a $(2+1)$-dimensional manifold. The dashed curve on the left represents fluctuations around the classical embedding, which, on-shell, is mapped to the classical embedding with a ${\rm Diff}_2$ transformation. This ${\rm Diff}_2$ is obtained from the ${\rm Diff}_3$ transformation of the embedding space ${\cal M}_{2+1}$. Here, ${\cal M}_{2+1} \equiv {\rm AdS}_3$.