Evidence for a $4$-dimensional $\mathcal{N}=1$ integrable quiver in massive type IIA

TL;DR

This paper investigates a family of massive type IIA supergravity backgrounds with warped AdS_5 factors, providing evidence that a special solution within this family exhibits classical integrability, unlike the others which are non-integrable and chaotic.

Contribution

It identifies a unique integrable solution in a family of massive type IIA backgrounds dual to 4D N=1 quiver theories, and analyzes its integrability properties.

Findings

One specific solution is integrable, others are non-integrable.

Numerical analysis shows chaotic behavior in non-integrable cases.

Analytic evidence supports integrability of the special solution.

Abstract

We are examining a newly discovered parametric family of backgrounds in massive type IIA supergravity that contains a warped $\text{AdS}_5$ factor. This family is the dual gravity description of $4$-dimensional quivers with $\mathcal{N}=1$ supersymmetry. We are interested in the status of classical integrability in these theories and we show that there exists a single choice of solutions that is special, while all other choices lead to non-integrable quivers and chaotic string motion. By focusing on this special choice we provide strong suggestive evidence for the integrability of the dual field theory based on analytic studies and extensive numerical analysis.