Type IIB supergravity solution for the T-dual of the η-deformed AdS 5 × S 5 superstring

B Hoare,A A Tseytlin

doi:10.1007/jhep10(2015)060

Abstract

We find an exact type IIB supergravity solution that represents a one-parameter deformation of the T-dual of the AdS 5 × S 5 background (with T-duality applied in all 6 abelian bosonic isometric directions). The non-trivial fields are the metric, dilaton and RR 5-form only. The latter has remarkably simple “undeformed” form when written in terms of a “deformation-rotated” vielbein basis. An unusual feature of this solution is that the dilaton contains a linear dependence on the isometric coordinates of the metric precluding a straightforward reversal of T-duality. If we still formally dualize back, we find exactly the metric, B-field and product of dilaton with RR field strengths as recently extracted from the η-deformed AdS 5 × S 5 superstring action in arXiv:1507.04239 . We also discuss similar solutions for deformed AdS n × S n backgrounds with n = 2, 3. In the η → i limit we demonstrate that all these backgrounds can be interpreted as special limits of gauged WZW models and are also related to (a limit of) the Pohlmeyer-reduced models of the AdS n × S n superstrings.

Highlights

We find an exact type IIB supergravity solution that represents a oneparameter deformation of the T-dual of the AdS5 × S5 background
The metric that originated from this singular limit of the λ-model metric was not the η-deformed AdS5 ×S5 metric itself but its T-dual with respect to all 6 isometric directions associated to Cartan generators of SO(2, 4) × SO(6)
Guided by the existence of a supergravity solution that supports the metric of the AdS5 × S5 λ-model by a simple dilaton and just the RR 5-form flux [14, 15], in [13] we applied the above singular limit to its AdS2 × S2 counterpart and found a new supergravity solution that supports the T-dual of the η-deformed AdS2 × S2 metric by a RR 2-form flux and factorized dilaton

Summary

Published for SISSA by Springer

Type IIB supergravity solution for the T-dual of the η-deformed AdS5 × S5 superstring. AInstitut fur Physik und IRIS Adlershof, Humboldt-Universitat zu Berlin, Zum Großen Windkanal 6, 12489, Berlin, Germany bThe Blackett Laboratory, Imperial College, London SW7 2AZ, U.K

In section

5Note that the singular term in

Fmpq Fn pq

Summary and concluding remarks