Non-integrability and chaos with unquenched flavor

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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=2 $$\end{document} 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.