Type II Solutions on AdS$_3\times S^3\times S^3$ with Large Superconformal Symmetry

TL;DR

This work constructs and classifies all local Type II AdS$_3$ solutions with large $\mathcal{N}=(4,0)$ supersymmetry realized by an $SO(4)$ R-symmetry on $S^3\times S^3$, using a bi-spinor/G-structure framework and an explicit $SO(4)$ spinor. It yields two globally compact examples: a massive IIA background with D8/O8 backreaction on $AdS_3\times S^3\times S^3\times S^1$, and a Type IIB background with D5s and O5s backreacting on $AdS_3\times S^3\times \mathbb{R}^4$, including cases with small $\mathcal{N}=(4,0)$ and potential $\mathcal{N}=(4,4)$ enhancement. In the IIA Case II and IIB Case II, local solutions featuring $\mathcal{N}=(4,4)$ or $\mathcal{N}=(4,0)$ are found, though some are non-compact or involve diminishingly controlled dilatons; the study also discusses possible gluing with defects to obtain global compactness and connects the central charges to the levels of the $d(2,1,alpha)$ superconformal algebra. The results broaden the landscape of AdS$_3$/CFT$_2$ duals with extended SUSY, providing new local building blocks and global gluing strategies toward candidate dual CFTs with large superconformal symmetry.

Abstract

New local solutions in type II supergravity that are foliations of AdS$_3\times S^3\times S^3$ over an interval and preserve at least large $\mathcal{N}=(4,0)$ supersymmetry are found. Some cases have compact internal space, some not and one experiences an enhancement to $\mathcal{N}=(4,4)$. We present two new globally compact solutions with D brane and O plane sources explicitly, one in each of IIA and IIB. The former is part of an infinite family of solutions with D8/O8s back reacted on AdS$_3\times S^3\times S^3\times S^1$. In the latter the the algebra degenerates to small $\mathcal{N}=(4,0)$ and the internal geometry is bounded between D5s and O5s back reacted on AdS$_3\times S^3\times \mathbb{R}^4$.