Supergravity backgrounds for deformations of AdS_n x S^n supercoset string models

TL;DR

This paper constructs and analyzes supergravity backgrounds corresponding to deformed AdS_n x S^n supercoset string models, exploring their solutions, field content, and singularity structures across different dimensions.

Contribution

It provides explicit supergravity solutions for deformed AdS_2 x S^2 and AdS_3 x S^3 models, and partial results for AdS_5 x S^5, linking these to the deformation parameter and supercoset models.

Findings

Deformed AdS_2 x S^2 background extends to a full supergravity solution.

Full solutions in AdS_3 x S^3 exist only for specific parameter values.

Partial solutions for AdS_5 x S^5 suggest more complex RR field support.

Abstract

We consider type IIB supergravity backgrounds corresponding to the deformed AdS_n x S^n supercoset string models of the type constructed in arXiv:1309.5850 which depend on one deformation parameter \k. In AdS_2 x S^2 case we find that the deformed metric can be extended to a full supergravity solution with non-trivial dilaton, RR scalar and RR 5-form strength. The solution depends on a free parameter (called a) that should be chosen as a particular function of \k to correspond to the deformed supercoset model. In AdS_3 x S^3 case the full solution supported by the dilaton, RR scalar and RR 3-form strength exists only in the two special cases of a=0 and a=1. We conjecture that there may be a more general one-parameter solution supported by several RR fields that for particular a=a(\k) corresponds to the supercoset model. In the most complicated deformed AdS_5 x S^5 case we were able to find only the expressions for the dilaton and the RR scalar. The full solution is likely to be supported by a combination of the 5-form and 3-form RR field strengths. We comment on the singularity structure of the resulting metric and exact dilaton field.