The $\mathrm{AdS}_5 \times \mathrm{S}^5$ mirror model as a string

TL;DR

This paper interprets the AdS5×S5 mirror model as a free string on a different background related by T duality, revealing hidden supersymmetry and connecting to integrable deformations, thus advancing understanding in AdS/CFT integrability.

Contribution

It demonstrates that the mirror theory can be viewed as a free string on a background related by T duality and reveals hidden supersymmetry, linking mirror models to integrable deformations.

Findings

Mirror theory corresponds to a free string on a T dual background.

The background is related to dS5×H5 with hidden supersymmetry.

Mirror duality is proven at the bosonic level for deformed models.

Abstract

Doing a double Wick rotation in the worldsheet theory of the light cone $\mathrm{AdS}_5 \times \mathrm{S}^5$ superstring results in an inequivalent, so-called mirror theory that plays a central role in the field of integrability in AdS/CFT. We show that this mirror theory can be interpreted as the light cone theory of a free string on a different background. This background is related to $\mathrm{dS}_5 \times \mathrm{H}^5$ by a double T duality, and has hidden supersymmetry. The geometry can also be extracted from an integrable deformation of the $\mathrm{AdS}_5 \times \mathrm{S}^5$ sigma model, and we prove the observed mirror duality of these deformed models at the bosonic level as a byproduct. While we focus on $\mathrm{AdS}_5 \times \mathrm{S}^5$, our results apply more generally.