The non-integrability of $L^{a,b,c}$ quiver gauge theories

TL;DR

This paper demonstrates that the string dynamics in the $AdS_5 imes L^{a,b,c}$ background are chaotic and non-integrable, indicating complex behavior in the dual quiver gauge theories.

Contribution

It provides the first evidence of non-integrability in $L^{a,b,c}$ quiver gauge theories through analytical and numerical methods.

Findings

String fluctuations are non-integrable and chaotic.

Numerical analysis shows positive Lyapunov exponents.

Point-like string limit corresponds to BPS mesons.

Abstract

We show that the $AdS_5 \times L^{a,b,c}$ solution in type IIB theory is non-integrable. To do so, we consider a string embedding and study its fluctuations which do not admit Liouville integrable solutions. We, also, perform a numerical analysis to study the time evolution of the string and compute the largest Lyapunov exponent. This analysis indicates that the string motion is chaotic. Finally, we consider the point-like limit of the string that corresponds to BPS mesons of the quiver theory.