M -strings and AdS3 solutions to M-theory with small N = (0,4) supersymmetry

We construct a general class of (small) N = (0, 4) superconformal solutions in M-theory of the form AdS(3)x S-3/Z(k)x CY2, foliated over an interval. These solutions describe M-strings in M5-brane intersections. The M -strings support (0, 4) quiver CFTs that are in correspondence with our backgrounds. We compute the central charge and show that it scales linearly with the total number of M -strings. We introduce momentum charge, thus allowing for a description in terms of M(atrix) theory. Upon reduction to Type IIA, we find a new class of solutions with four Poincare supercharges of the form AdS(2)x S(3)x CY(2)x I , that we extend to the massive IIA case. We generalise our constructions to provide a complete class of AdS(3) solutions to M-theory with (0,4) supersymmetry and SU(2) structure. We also construct new AdS(2)x S(3)x M(4)x I solutions to massive IIA, with M-4 a 4d Kahler manifold and four Poincare supercharges.