We study AdS 3 × S 2 solutions in massive IIA that preserve small 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 ×S 2 ×M 4 ×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 D3branes 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 × S 2 × 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 × S 3 × 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.

In this paper we discuss an infinite family of new solutions in massive Type IIA supergravity with AdS 3 ×S 2 factors, preserving N = (0, 4) SUSY. After studying geometrical aspects of the backgrounds we propose a duality with a precise family of quivers that flow to (0,4) fixed points at low energies. These quivers consist on two families of (4,4) linear quivers coupled by matter fields. We present various tests of our proposal.Dedicated to the memory of Steven S. Gubser. 1 ylozano@uniovi.es 2

We discuss new solutions in massive type IIA supergravity with AdS 3 × S 2 factors, preserving N ¼ ð0; 4Þ supersymmetry. We propose a duality with a precise family of quivers that flow to N ¼ ð0; 4Þ fixed points at low energies. These quivers consist on two families of linear quivers coupled by matter fields. Physical observables such as the central charges provide stringent checks of the proposed duality. A formal mapping is presented connecting our backgrounds with those dual to six dimensional N ¼ ð1; 0Þ conformal field theories (CFTs), suggesting the existence of a flow across dimensions between the CFTs.