$\mathcal{N}=6$ supersymmetric AdS${}_2\times {\mathbb{CP}}^3\times {\Sigma }_2$

Abstract

We perform a complete classification of AdS${}_2$ solutions of Type II supergravity realising $\mathcal{N}=6$ supersymmetry and OSp$(6|2)$ superconformal symmetry on backgrounds that are foliations of AdS${}_2\times {\mathbb{CP}}^3$ over a Riemann surface ${\Sigma }_2$. Such solutions only exist in type IIB supergravity and are in 1 to 1 correspondence with a fourth order PDE that can be locally solved in terms of two holomorphic functions. Particular solutions in the class are the T-duals of the ${\text{AdS}}_3\times {\mathbb{CP}}^3$ and ${\text{AdS}}_2\times {\text{S}}^7$ solutions to massive Type IIA supergravity found in the literature. We discuss the field theory interpretation of the two sub-classes of solutions related to ${\text{AdS}}_3\times {\mathbb{CP}}^3$ by Abelian and non-Abelian T-duality, which provide explicit examples for the Riemann surface an annulus or a strip. In the second case we interpret the solutions as holographic duals to baryon vertex configurations realised in D2-brane box models.

30 pages + appendices v2, refernence added, published version