Two-parameter integrable deformations of the AdS₃× S³× T⁴ superstring

For supercosets with isometry group of the form $\hat{G}$×$\hat{G}$, the η-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 back- grounds for the two-parameter integrable deformation of the AdS₃× S³× T⁴ 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.