Poisson-Lie duals of the $\eta$-deformed ${\mathrm{AdS}}_2\times {\mathrm{S}}^2\times {\mathrm{T}}^6$ superstring

Abstract

We investigate Poisson-Lie duals of the $\eta$-deformed ${\mathrm{AdS}}_2\times {\mathrm{S}}^2\times {\mathrm{T}}^6$ superstring. The $\eta$-deformed background satisfies a generalisation of the type II supergravity equations. We discuss three Poisson-Lie duals, with respect to (i) the full $\mathfrak{psu}(1,1|2)$ superalgebra, (ii) the full bosonic subalgebra and (iii) the Cartan subalgebra, for which the corresponding backgrounds are expected to satisfy the standard type II supergravity equations. The metrics and B-fields for the first two cases are the same and given by an analytic continuation of the $\lambda$-deformed model on ${\mathrm{AdS}}_2\times {\mathrm{S}}^2\times {\mathrm{T}}^6$ with the torus undeformed. However, the RR fluxes and dilaton will differ. Focusing on the second case we explicitly derive the background and show agreement with an analytic continuation of a known embedding of the $\lambda$-deformed model on ${\mathrm{AdS}}_2\times {\mathrm{S}}^2$ in type II supergravity.

37 pages, published version