AdS$_3$ solutions in Massive IIA with small $\mathcal{N}=(4,0)$ supersymmetry

TL;DR

The paper addresses the construction of AdS_3 imes S^2 solutions in massive IIA that preserve small N=(4,0) supersymmetry by building spinors transforming under an SU(2)_R and deriving two consistent geometric classes. Class I requires a conformal Calabi-Yau 2-fold base CY_2, while Class II allows a Kahler M_4 base, with explicit local warp-factor structures and fluxes; T-duality yields IIB AdS_3 imes S^3 imes M_4 solutions including generalizations of the D1-D5-KK near-horizon and D3-branes wrapping curves in elliptic CY_3 bases with nontrivial 3-form flux. The authors further uncover numerous local AdS_3 imes S^2 imes CY_2 foliations over intervals, which can be glued into global solutions using defect branes, enabling infinite families of globally compact backgrounds. These constructions furnish new holographic playgrounds for two-dimensional (0,4) CFTs and illuminate broader AdS/CFT contexts, with strong links to known D-brane systems and F-theory geometries via T-duality and Calabi–Yau flux frameworks.

Abstract

We study AdS$_3\times \text{S}^2$ solutions in massive IIA that preserve small ${\cal N}=(4,0)$ supersymmetry in terms of an SU(2)-structure on the remaining internal space. We find two new classes of solutions that are warped products of the form AdS$_3\times \text{S}^2\times \text{M}_4\times \mathbb{R}$. For the first, M$_4$=CY$_2$ and we find a generalisation a D4-D8 system involving possible additional branes. For the second, M$_4$ need only be Kahler, and we find a generalisation of the T-dual of solutions based on D3-branes wrapping curves in the base of an elliptically fibered Calabi-Yau 3-fold. Within these classes we find many new locally compact solutions that are foliations of AdS$_3\times \text{S}^2\times\text{CY}_2$ over an interval, bounded by various D brane and O plane behaviours. We comment on how these local solutions may be used as the building blocks of infinite classes of global solutions glued together with defect branes. Utilising T-duality we find two new classes of AdS$_3\times \text{S}^3\times \text{M}_4$ solutions in IIB. The first backreacts D5s and KK monopoles on the D1-D5 near horizon. The second is a generalisation of the solutions based on D3-branes wrapping curves in the base of an elliptically fibered CY$_3$ that includes non trivial 3-form flux.