Two-parameter integrable deformations of the $Ad{S}_3\times S^3\times T^4$ superstring

Abstract

For supercosets with isometry group of the form $\hat{G}\times \hat{G}$, the eta-deformation can be generalised to a two-parameter integrable deformation with independent $q$-deformations of the two copies. We study its kappa-symmetry and write down a formula for the Ramond-Ramond fluxes. We then focus on $\hat{G}=PSU(1,1|2)$ and construct two supergravity backgrounds for the two-parameter integrable deformation of the $Ad{S}_3\times S^3\times T^4$ superstring, as well as explore their limits. We also construct backgrounds that are solutions of the weaker generalised supergravity equations of motion and compare them to the literature.

32 pages, 2 figures, published version