Aspects of 7d and 6d gauged supergravities



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We determine the conditions under which half-maximal matter coupled gauged supergravity in seven dimensions admits a chiral circle reduction to yield a matter coupled gauged supergravity in six dimensions with 8 real supersymmetry. Solving these conditions we nd that the SO(2; 2) and SO(3; 1) gauged 7D supergravities give a U(1)R, and the SO(2; 1) gauged 7D supergravity gives an Sp(1)R gauged chiral 6D supergravity coupled to certain matter multiplets. In the 6D models obtained, with or without gauging, we show that the scalar fields of the matter sector parametrize the coset SO(p + 1; 4)=SO(p + 1) SO(4), with the (p + 3) axions corresponding to its abelian isometries. We then derive the necessary and sufficient conditions for the existence of a Killing spinor in N = (1; 0) gauge 6D supergravity coupled to a single tensor multiplet, vector multiplets and hypermultiplets. We show that these conditions imply most of the eld equations. We also determine the remaining equations that need to be satised by an exact solution. In this framework, we nd a novel 1=8 supersymmetric dyonic string solution with nonvanishing hypermultiplet scalars. The activated scalars parametrize a 4 dimensional submanifold of a quaternionic hyperbolic ball. The key point is that we employ an identity map between this submanifold and the internal space transverse to the string worldsheet, thereby nding a higher dimensional generalization of Gell- Mann-Zweibach tear-drop solution.