Non-integrability and Chaos with Unquenched Flavor

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.

34 pages, 6 figures; v2: minor additions, references added

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• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
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• Chaotic spin chains in AdS/CFT
• Constraining integrable AdS/CFT with factorized scattering
• Circular string in a Black p-brane leading to chaos
• Non-integrability of the $\Omega$-deformation
• Interplay of magnetic field and chemical potential induced anisotropy and frame dependent chaos of a $Q\bar{Q}$ pair in holographic QCD
• Analytic integrability for holographic duals with $J\bar{T}$ deformations
• Integrability structures in string theory
• Investigating (Non)-Integrability and Pulsating String in D3-Brane Background