3D gauged supergravity from SU(2) reduction of N = 1 6D supergravity

Abstract

We obtain Yang-Mills SU(2) × G gauged supergravity in three dimensions from SU(2) group manifold reduction of (1,0) six dimensional supergravity coupled to an anti-symmetric tensor multiplet and gauge vector multiplets in the adjoint of G. The reduced theory is consistently truncated to N = 4 3D supergravity coupled to 4(1+dimG) bosonic and 4(1 + dimG) fermionic propagating degrees of freedom. This is in contrast to the reduction in which there are also massive vector fields. The scalar manifold is \( R \times \frac{{{\text{SO}}\left( {3,\,\dim G} \right)}}{{{\text{SO}}(3) \times {\text{SO}}\left( {\dim G} \right)}} \), and there is a SU(2)×G gauge group. We then construct N = 4 Chern-Simons (SO(3) ⋉ R 3) (G ⋉ R dimG) three dimensional gauged supergravity with scalar manifold \( \frac{{{\text{SO}}\left( {4,1 + \dim G} \right)}}{{{\text{SO}}(4) \times {\text{SO}}\left( {1 + \dim G} \right)}} \) and explicitly show that this theory is on-shell equivalent to the Yang-Mills SO(3)×G gauged supergravity theory obtained from the SU(2) reduction, after integrating out the scalars and gauge fields corresponding to the translational symmetries R 3 × R dimG.