Abstract
We elevate λ-deformed σ-models into full type-II supergravity backgrounds. We construct several solutions which contain undeformed AdSn spaces, with n=2,3,4 and 6, as an integrable part. In that respect, our examples are the first in the literature in this context and bring λ-deformations in contact with the AdS/CFT correspondence. The geometries are supported by appropriate dilaton and RR-fields. Most of the solutions admit non-Abelian T-dual limits.
Highlights
We elevate λ-deformed σ-models into full type-II supergravity backgrounds
In parallel to the above, a class of integrable σ-models was introduced in [14,15,16] and [17,18,19] for group and coset spaces, respectively. These are connected to the Principal Chiral Model (PCM) for groups and cosets which are integrable
Having a σ-model, let alone an integrable one, it is very important to elevate it into a full supergravity solution
Summary
We review the λ-deformed models based on the coset SU(2)/U(1) CFT constructed in [1]. By analytic continuation we obtain the corresponding λ-deformed models based on the SL(2, R)/U(1) and SL(2, R)/SO(1, 1) exact coset CFTs. ds2 = k dβ2 + cot β dα. Where ηab is the Minkowski metric with signature (−, +) This will be instrumental in constructing type-II supergravity solutions in which the background CS2λ will be an integrable part. Note that (2.9) is frame-dependent since the right hand side is proportional to ηab even though the metric is of Euclidean signature. The above information allows one to get already an idea of the curvature of the space M6 This can be done by re-writing the dilaton equation (A.4) as RM6 + βΦCS2λ + βΦCH2,λ = 0 , which due to (2.9) and (2.21) implies for its Ricci scalar that (3.3)
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