Interpolating families of integrable AdS3 backgrounds

TL;DR

This paper constructs integrable deformations interpolating between various AdS3 backgrounds, preserving half of the supersymmetry, using TsT transformations, and demonstrates their integrability through gauge fixing and Hamiltonian analysis.

Contribution

It introduces a method to generate integrable interpolations between AdS3 backgrounds via TsT transformations, preserving supersymmetry and facilitating quantum integrability analysis.

Findings

Constructed interpolating backgrounds between different AdS3 geometries.

Preserved half of the supersymmetry in all interpolations.

Demonstrated integrability through gauge fixing and Hamiltonian computation.

Abstract

We construct families of integrable deformations that interpolate between $AdS_3\times S^3\times S^3\times S^1$ and either $AdS_3\times S^3\times S^2\times T^2$ or $AdS_3\times S^2\times S^2\times T^3$. They preserve half of the supersymmetry of the original background, namely one copy of the $\mathfrak{d}(2,1;\alpha)$ algebra. From this it follows a similar integrable interpolation between $AdS_3\times S^3\times T^4$ and $AdS_3\times S^2\times T^5$, which also preserves half of the supersymmetry, namely a copy of the $\mathfrak{psu}(1,1|2)$ algebra. In all cases, the interpolating backgrounds are constructed by using TsT transformations, which makes it easy to implement them in the integrability formalism in the full quantum theory. To illustrate this point, we discuss the lightcone gauge fixing of the models and compute their pp-wave Hamiltonian.