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Poisson-Lie duals of the \(\eta\)-deformed \(\mathrm{AdS}_{2} \times S^2 \times T^6\) superstring. (English) Zbl 1396.83052

Summary: We investigate Poisson-Lie duals of the \(\eta\)-deformed \(\mathrm{AdS}_{2} \times S^2 \times T^6\) 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 \( \mathfrak{p}\mathfrak{s}\mathfrak{u}(1,1 | 2)\) 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 \(\mathrm{AdS}_{2} \times S^2 \times T^6\) 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 \(\mathrm{AdS}_{2} \times S^2\) in type II supergravity.

MSC:

83E30 String and superstring theories in gravitational theory
81R12 Groups and algebras in quantum theory and relations with integrable systems
83E50 Supergravity
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