Nonintegrability of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>L</mml:mi><mml:mrow><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:msup></mml:math> quiver gauge theories

Abstract

We show that the ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{L}^{a,b,c}$ solution in type IIB theory is nonintegrable. 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 pointlike limit of the string that corresponds to Bogomol'nyi-Prasad-Sommerfied mesons of the quiver theory.

Topics & Concepts