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

Understand

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 $AdS_5 \times S^5$.