PoissonLie duals of the $\eta$deformed $\mathrm{AdS}_2 \times \mathrm{S}^2 \times \mathrm{T}^6$ superstring
Abstract
We investigate PoissonLie 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 PoissonLie duals, with respect to (i) the full $\mathfrak{psu}(1,12)$ 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 Bfields 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.
 Publication:

arXiv eprints
 Pub Date:
 July 2018
 arXiv:
 arXiv:1807.04608
 Bibcode:
 2018arXiv180704608H
 Keywords:

 High Energy Physics  Theory
 EPrint:
 37 pages, published version