Yang-Mills-Chern-Simons Supergravity

Abstract

N=(1,0) supergravity in six dimensions admits AdS_3\times S^3 as a vacuum solution. We extend our recent results presented in hep-th/0212323, by obtaining the complete N=4 Yang-Mills-Chern-Simons supergravity in D=3, up to quartic fermion terms, by S^3 group manifold reduction of the six dimensional theory. The SU(2) gauge fields have Yang-Mills kinetic terms as well as topological Chern-Simons mass terms. There is in addition a triplet of matter vectors. After diagonalisation, these fields describe two triplets of topologically-massive vector fields of opposite helicities. The model also contains six scalars, described by a GL(3,R)/SO(3) sigma model. It provides the first example of a three-dimensional gauged supergravity that can obtained by a consistent reduction of string-theory or M-theory and that admits AdS_3 as a vacuum solution. There are unusual features in the reduction from six-dimensional supergravity, owing to the self-duality condition on the 3-form field. The structure of the full equations of motion in N=(1,0) supergravity in D=6 is also elucidated, and the role of the self-dual field strength as torsion is exhibited.