Supergravity realisations of $λ$-models

TL;DR

The work develops ten-dimensional type-II supergravity backgrounds that implement multiple copies and mixings of $\lambda$-deformed coset CFTs on $\mathrm{SO}(n+1)_k/\mathrm{SO}(n)_k$ for $n=2,3,4$, with an emphasis on undeformed AdS factors to connect to holography. By judiciously choosing Ramond–Ramond flux ansätze, the authors turn the supergravity equations of motion into a set of algebraic constraints on constant flux parameters, enabling explicit constructions of rich geometries such as $AdS_6$, $AdS_4\times H_2$, $AdS_3\times H_3$, and $AdS_2$-based products that mix CS$^n_{\lambda}$ factors. Real-valued solutions impose bounds on the deformation parameter $\lambda$, which in several cases exclude $\lambda=0$ (undeformed limit) or $\lambda\to1$ (NATD limit), highlighting nontrivial holographic backgrounds beyond the standard limits. The paper provides a catalog of representative backgrounds across all $n=2,3,4$ and shows how to generate further examples via RR-parameter choices, suggesting potential holographic duals and motivating future work on supersymmetry, stability, and brane-constructed realizations.

Abstract

We construct solutions of type-II supergravity based on multiple copies and/or mixings of $λ$-deformed coset CFTs on $\mathrm{SO}(n+1)_k/\mathrm{SO}(n)_k$, with $n = 2, 3, 4$. The resulting ten-dimensional geometries contain undeformed $\mathrm{AdS}$ factors, thereby allowing a connection between $λ$-deformations and the AdS/CFT correspondence. Imposing reality conditions on the solutions further constrains the deformation parameter. In some cases these bounds exclude the undeformed ($λ= 0$) or non-Abelian T-dual ($λ\to 1$) limits. This work extends the results of 1911.12371 and 2411.11086.