New ${\cal N} = 1$ supersymmetric $AdS_5$ backgrounds in Type IIA supergravity

TL;DR

We construct a new family of ${\cal N}=1$ AdS$_5$ backgrounds in Type IIA by applying non-Abelian T-duality to the $Y^{p,q}$ Sasaki--Einstein spaces, yielding smooth geometries with an $SU(2)$ structure that lift to M-theory. The work provides explicit geometric data, including frames, the dilaton $e^{-2\Phi}=\Delta$, the NS two-form $B_2$, and RR fluxes $F_2$, $F_4$, and verifies the solutions satisfy Type IIA supergravity equations; a D6 Page charge is finite and equals $\sqrt{2}\pi\mathrm{Vol}(Y^{p,q})$, indicating a D3 charge from the seed geometry is converted under duality. The M-theory lift reveals an internal six-manifold ${\cal M}_6$ with an $SU(2)$ structure, described by forms $J_2$, $\Omega_2$, and one-forms $K^1,K^2$, compatible with Gauntlett-type classifications; however, the six-manifold is not globally complex. The authors discuss global/topological issues and potential holographic interpretations in Sicilian-type theories, highlighting open questions about the global completion and dual CFT data.

Abstract

We present a family of N=1 supersymmetric backgrounds in type-IIA supergravity and their lifts to eleven-dimensional supergravity. These are of the form $AdS_5 \times X^5$ and are characterised by an $SU(2)$ structure. The internal space, $X^5$, is obtained from the known Sasaki-Einstein manifolds, $Y^{p,q}$, via an application of non-Abelian T-duality.