The general form of supersymmetric solutions of N = (1,0) U(1) and SU(2) gauged supergravities in six dimensions

We obtain necessary and sufficient conditions for a supersymmetric field configuration in the N = (1, 0) U (1) or SU(2) gauged supergravities in W six dimensions, and impose the field equations on this general ansatz. It is found that any supersymmetric solution is associated with an SU(2) x R-4 structure. The structure is characterized by a null Killing vector which induces a natural 2 + 4 split of the six-dimensional spacetime. A suitable combination of the field equations implies that the scalar curvature of the four-dimensional Riemannian part, referred to as the base, obeys a second-order differential equation; surprisingly, for a large class of solutions the equation in the SU(2) theory requires the vanishing of the Weyl anomaly of N = 4 SYM on the base. Bosonic fluxes introduce torsion terms that deform the SU(2) x R-4 structure away from a covariantly constant one. The most general structure can be classified into terms of its intrinsic torsion. For a large class of solutions the gauge field strengths admit a simple geometrical interpretation: in the U(1) theory the base is Kahler, and the gauge field strength is the Ricci form; in the SU(2) theory, the gauge field strengths are identified with the curvatures of the left-hand spin bundle of the base. We employ our general ansatz to construct new solutions; we show that the U(1) theory admits a symmetric Cahen-Wallach(4) x S-2 solution together with a compactifying pp-wave. The SU(2) theory admits a black string, whose near horizon limit is AdS(3) x S-3, which is supported by a self-dual 3-form flux and a meron on the S-3. In the limit of the zero 3-form flux we obtain the Yang-Mills analogue of the Salam-Sezgin solution of the U(l) theory, namely R-1,R-2 x S-3. Finally we obtain the additional constraints implied by enhanced supersymmetry, and discuss Penrose limits in the theories.