A supersymmetric consistent truncation for conifold solutions

We establish a supersymmetric consistent truncation of type IIB supergravity on the T¹ coset space, based on extending the Papadopoulos-Tseytlin ansatz to the full set of SU(2)×SU(2) invariant Kaluza-Klein modes. The five-dimensional model is a gauged N=4 supergravity with three vector multiplets, which incorporates various conifold solutions and is suitable for the study of their dynamics. By analysing the scalar potential we find a family of new non-supersymmetric AdS₅ extrema interpolating between a solution obtained long ago by Romans and a solution employing an Einstein metric on T¹ different from the standard one. Finally, we discuss some simple consistent subtruncations preserving N=2 supersymmetry. One of them still contains the Klebanov-Strassler solution, and is compatible with the inclusion of smeared D7-branes.