Supergravity background of λ-deformed model for AdS 2 × S 2 supercoset

摘要

Starting with the F ? / G supercoset model corresponding to the AdS n × S n superstring one can define the λ -model of arXiv:1409.1538 either as a deformation of the F ? / F ? gauged WZW model or as an integrable one-parameter generalisation of the non-abelian T-dual of the AdS n × S n superstring sigma model with respect to the whole supergroup F ? . Here we consider the case of n = 2 and find the explicit form of the 4d target space background for the λ -model for the PSU ( 1 , 1 | 2 ) / SO ( 1 , 1 ) × SO ( 2 ) supercoset. We show that this background represents a solution of type IIB 10d supergravity compactified on a 6-torus with only metric, dilaton Φ and the RR 5-form (represented by a 2-form F in 4d) being non-trivial. This implies that the λ -model is Weyl invariant at the quantum level and thus defines a consistent superstring sigma model. The supergravity solution we find is different from the one in arXiv:1410.1886 which should correspond to a version of the λ -model where only the bosonic subgroup of F ? is gauged. Still, the two solutions have equivalent scaling limit of arXiv:1504.07213 leading to the isometric background for the metric and e Φ F which is related to the η -deformed AdS 2 × S 2 sigma model of arXiv:1309.5850. Similar results are expected in the AdS 3 × S 3 and AdS 5 × S 5 cases.