Non-integrability in AdS$_3$ vacua

TL;DR

This paper investigates classical integrability of certain AdS3 supergravity vacua in massive IIA and IIB theories, finding non-integrability in most cases except for known integrable solutions.

Contribution

It applies an analytic non-integrability method to a broad class of AdS3 vacua, demonstrating non-integrability for most solutions and confirming integrability only in specific known cases.

Findings

Most supergravity solutions are non-integrable.

Known integrable solutions include AdS3×S3×S˜3×S1 and AdS3×S3×T4.

Method confirms non-integrability via string fluctuation analysis.

Abstract

We ask the question of classical integrability for certain (classes of) supergravity vacua that contain an AdS$_3$ factor arising in massive IIA and IIB theories and realizing various and different amounts of supersymmetry. Our approach is based on a well-established method of analytic non-integrability for Hamiltonian systems. To detect a non-integrable sector we consider a non-trivially wrapped string soliton and study its fluctuations. We answer in the negative for each and every one of the supergravity solutions. That is, of course, modulo very specific limits where the metrics reduce to the AdS$_3 \times$ S$^3 \times \tilde{S}^3 \times$ S$^1$ and AdS$_3 \times$ S$^3 \times$ T$^4$ solutions which are known to be integrable.