Integrability and non-Integrability in N=2 SCFTs and their Holographic Backgrounds

TL;DR

This paper investigates the classical integrability of string worldsheet theories in holographic duals of N=2 SCFTs, finding that most are non-integrable except for specific cases like non-Abelian T-duals of AdS5×S5.

Contribution

It demonstrates the generic non-integrability of Gaiotto-Maldacena backgrounds and identifies exceptions where classical integrability is preserved.

Findings

Numerical evidence of non-zero Lyapunov exponents indicating chaos.

Analytic failure to find Liouvillian solutions for the Normal Variational Equation.

Non-Abelian T-dual of AdS5×S5 retains classical integrability.

Abstract

We show that the string worldsheet theory of Gaiotto-Maldacena holographic duals to N=2 superconformal field theories generically fails to be classically integrable. We demonstrate numerically that the dynamics of a winding string configuration possesses a non-vanishing Lyapunov exponent. Furthermore an analytic study of the Normal Variational Equation fails to yield a Liouvillian solution. An exception to the generic non-integrability of such backgrounds is provided by the non-Abelian T-dual of $AdS_5 \times S^5$. Here by virtue of the canonical transformation nature of the T-duality classical integrability is known to be present.