Non-integrability and Chaos with Unquenched Flavor

TL;DR

This paper investigates how adding unquenched flavor to certain gauge theories affects their integrability and chaos, revealing that flavor backreaction induces non-integrability and chaos saturation in string dynamics.

Contribution

It demonstrates that unquenched flavor breaks integrability in gravity duals and shows chaos saturation with increasing flavor number, providing new insights into gauge/string duality.

Findings

Unquenched flavor induces non-integrability in gravity duals.

Lyapunov exponent saturates as flavor number increases.

Chaos effects do not intensify beyond a certain flavor threshold.

Abstract

We study (non-)integrability and the presence of chaos in gravity dual backgrounds of strongly coupled gauge theories with unquenched flavor, specifically of the four-dimensional N=2 super Yang-Mills theory and the three-dimensional ABJM theory. By examining string motion on the geometries corresponding to backreacted D3/D7 and D2/D6 systems, we show that integrable theories with quenched flavor become non-integrable when the virtual quark loops are taken into account. For the string solutions in the backreacted D3/D7 system, we compute the leading Lyapunov exponent which turns out to saturate to a positive value as the number of flavors increases. The exponent depends very weakly on the number of flavors when they approach the number of colors. This suggests that once a particular flavor number in the theory is reached, a further increase does not lead to more severe chaotic phenomena, implying certain saturation effects on chaos.