$\mathcal{N}=6$ supersymmetric AdS$_2 \times \mathbb{CP}^3\times Σ_2 $

TL;DR

The paper achieves a complete classification of AdS$_2$ solutions in Type IIB supergravity preserving ${\cal N}=6$ supersymmetry and ${\rm OSp}(6|2)$, on backgrounds that are AdS$_2\times\mathbb{CP}^3$ fibred over a Riemann surface $\Sigma_2$. Beginning from Legramandi's ${\cal N}=1$ AdS$_2$ G-structure, the authors construct six ${\cal N}=1$ spinor bilinears realizing ${\rm SO}(6)$ on $\mathbb{CP}^3$, and solve the SUSY constraints to reduce the problem to a single real function $h$ on $\Sigma_2$ governed by a fourth-order PDE that can be expressed in terms of two holomorphic data ${\cal A}_{1,2}$. The general local solution is encoded in harmonic data, with explicit local forms for the metric, dilaton, NSNS flux and RR Page fluxes; two physically relevant subclasses are explored in detail: Abelian T-duals of AdS$_3\times\mathbb{CP}^3\times I$ yielding AdS$_2\times\mathbb{CP}^3\times S^1\times I$ and non-Abelian T-duals related to AdS$_2\times\mathbb{CP}^3\times I\times I'$, each with distinct brane constructions and dual 1d SCQMs. The authors compute holographic central charges and discuss the role of baryon-vertex configurations, Freed-Witten effects, and global completions, outlining open problems such as a direct field-theory derivation of the 1d central charge and a full geometric completion of the NATD class.

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 $Σ_2$. 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.

Figures (4)

• Figure 1: Brane configuration associated to the $\text{AdS}_3\times\mathbb{CP}^3\times I$ solutions. $N_l$ D3-branes stretch between $\psi=0$ and $\pi$ and $N_l+M_l$ between $\psi=\pi$ and $2\pi$. The details of the construction can be found in Lozano:2024idt.
• Figure 2: Quiver diagram associated to the $\text{AdS}_2\times \mathbb{CP}^3\times \text{S}^1\times I$ solutions. Circles denote $\mathcal{N}=4$ vector multiplets, black lines $\mathcal{N}=4$ twisted hypermultiplets, grey lines $\mathcal{N}=4$ hypermultiplets, grey dashed lines $\mathcal{N}=2$ Fermi multiplets and black dashed lines $\mathcal{N}=4$ Fermi multiplets.
• Figure 3: F1-strings stretched between Dp and D(8-p) branes.
• Figure 4: F1-strings stretched between the Dp and D(8-p) branes along the $\rho$-direction, in units of $Q'_{8-p}$.