Abstract
We investigate Poisson-Lie duals of the η-deformed AdS2 ×S2 ×T6 superstring. The η-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}left(1,left.1right|2right) 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 λ-deformed model on AdS2 × S2 × T6 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 λ-deformed model on AdS2 × S2 in type II supergravity.
Highlights
Its η-deformation [13, 14]
The semi-symmetric space sigma model describes a truncation of the type II Green-Schwarz superstring [15,16,17,18] on certain AdS2 × S2 × T6 supergravity backgrounds [19]
We derive the background of the Poisson-Lie dual of the η-deformed AdS2 × S2 × T6 superstring with respect to the full bosonic subalgebra su(1, 1) ⊕ su(2)
Summary
As for abelian and non-abelian duality, dual models can be obtained starting from an action for a dynamical field in the Drinfel’d double and integrating out half the degrees of freedom. To define this first-order action on the Drinfel’d double we extend the definition of the inner-product to the Grassmann envelope of the superalgebra as. Starting from the action (2.9) and using the decomposition of the Drinfel’d double (2.1), where we recall both g and gare subalgebras, we recover the Poisson-Lie dual models on G and Gby integrating out the degrees of freedom associated to gand g respectively [25, 26]. We specialise to the supercoset (3.1), discussing the possible Poisson-Lie duals of the η-deformed AdS2 × S2 supercoset model
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