Integrability and non-integrability for marginal deformations of 4d $\mathcal N = 2$ SCFTs

TL;DR

This paper investigates how marginal deformations affect the integrability of 4d $ ext{N}=2$ SCFTs, showing a transition from integrable to chaotic dynamics as deformation increases, with implications for string theory models.

Contribution

It demonstrates the transition from integrable to non-integrable behavior in deformed 4d $ ext{N}=2$ SCFTs and interprets the $ ext{gamma}$-deformation as an interpolation between different supersymmetric theories.

Findings

Chaos indicators increase with deformation, indicating chaos at large deformations.

Small deformations show non-chaotic, potentially integrable dynamics.

The $ ext{gamma}$-deformation interpolates between integrable $ ext{N}=2$ and non-integrable $ ext{N}=1$ SCFTs.

Abstract

We study integrability and non-integrability for marginal deformations of 4d $\mathcal N =2$ SCFTs. We estimate various chaos indicators for the bulk theory which clearly shows the onset of a chaotic string dynamics in the limit of large deformations. On the other hand, for small values of the deformation parameter, the resulting dynamics exhibits a non-chaotic motion and therefore presumably an underlying integrable structure. Our analysis reveals that the $\gamma$-deformation in the type-IIA theory could be interpreted as an interpolation between a class of integrable $\mathcal N =2$ SCFTs and a class of non-integrable $\mathcal N =1$ SCFTs at strong coupling. We also generalise our results in the presence of the flavor branes.