On Type IIA AdS${}_3$ solutions and massive GK geometries

Abstract

We give the necessary and sufficient conditions for warped AdS${}_3$ (and Mink${}_3$) solutions of Type II supergravities to preserve $\mathcal{N}=(2,0)$ supersymmetry, in terms of geometric conditions on their internal space M${}_7$. Such solutions possess a canonical ten-dimensional Killing vector that can be either time-like or null. In this work we classify the null case in massive Type IIA supergravity which necessitates that M${}_7$ decomposes as a circle fibration over a six-dimensional base with orthogonal SU(2)-structure containing a complex four-manifold. We narrow our focus to solutions for which M${}_7$ becomes ${\mathbb{T}}^2$ fibred over a foliation of a Kähler manifold over an interval. We find a class of solutions which are the massive Type IIA version of GK geometries and present an extremal problem which computes the central charge of the solution using just topology. Finally, we present geometric conditions for AdS${}_3$ solutions to preserve arbitrary extended chiral supersymmetry.

References in corpus (18)

• Sasaki-Einstein Manifolds and Volume Minimisation
• Exact two-dimensional superconformal R-symmetry and c-extremization
• D3-branes wrapped on a spindle
• F-theory and AdS_3/CFT_2
• Comments on AdS2 solutions of D=11 Supergravity
• Geometries with Killing Spinors and Supersymmetric AdS Solutions
• No-scale and scale-separated flux vacua from IIA on G2 orientifolds
• Toric geometry and the dual of $c$-extremization
• Supersymmetric AdS3 X S2 M-theory geometries with fluxes
• New $\mathcal{N}=(0,4)$ AdS${}_3$ near-horizons in Type IIB
• Global geometry of the supersymmetric AdS_3/CFT_2 correspondence in M-theory
• Proving the equivalence of $c$-extremization and its gravitational dual for all toric quivers
• 1/4-BPS M-theory bubbles with SO(3) x SO(4) symmetry
• Fibred GK geometry and supersymmetric $AdS$ solutions
• Exact Half-BPS Flux Solutions in M-theory with $D(2,1;c^{\prime };0{)}^2$ Symmetry: Local Solutions
• Non-integrability in AdS${}_3$ vacua
• $\mathcal{I}$/$c$-Extremization in M/F-Duality
• AdS${}_3\times$ S${}^2$ in IIB with small $\mathcal{N}=(4,0)$ supersymmetry

Cited by in corpus (4)

• Scale-separated AdS${}_3$ vacua from $G_2$-orientifolds using bispinors
• AdS${}_2$ near-horizons, defects and string dualities
• $N=(2,0)$ AdS${}_3$ Solutions of M-theory
• New AdS${}_3$/CFT${}_2$ pairs in massive IIA with $(0,4)$ and $(4,4)$ supersymmetries