A supersymmetric consistent truncation for conifold solutions

Abstract

We establish a supersymmetric consistent truncation of type IIB supergravity on the T 1,1 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 AdS 5 extrema interpolating between a solution obtained long ago by Romans and a solution employing an Einstein metric on T 1,1 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.

Flowing from AdS5 to AdS3 with T 1,1

“…Expanding about the AdS 5 × T 1,1 vacuum these fields give rise to SU(2, 2|1) multiplets, consisting of the gravity multiplet, a hypermultiplet, a massive gravition multiplet and a massive vector multiplet. For the special case when SE 5 = T 1,1 , the D = 5 N = 4 gauged supergravity has an extra N = 4 "Betti" vector multiplet [9,10] (supersymmetry was discussed in [11]). Expanding about the AdS 5 × T 1,1 vacuum, the latter gives rise to a massless Betti vector multiplet, corresponding to the baryonic symmetry, as well as a Betti hypermultiplet.…”

“…Expanding about the AdS 5 × T 1,1 vacuum, the latter gives rise to a massless Betti vector multiplet, corresponding to the baryonic symmetry, as well as a Betti hypermultiplet. In fact the solutions that we have just constructed are actually solutions of a further truncation to an D = 5 N = 2 gauged supergravity theory in which one discards the fields associated with the massive gravitino multiplet and also the massless Betti vector multiplet (while keeping the Betti hypermultiplet) [9].…”

“…A key feature of the UV expansion (2.17) that is driving the supersymmetric flow, is that two D = 5 "axion" scalar fields (labelled by b Φ , c Φ in [9] and e 1 0 , e 2 0 in [11]) are equal to −λx 1 , λx 2 , respectively. These axions lie in the Betti hypermultiplet, which is identified with Tr(W 2 1 − W 2 2 ) in the dual SCFT [9,41], and are dual to marginal operators with dimension ∆ = 4.…”

“…These axions lie in the Betti hypermultiplet, which is identified with Tr(W 2 1 − W 2 2 ) in the dual SCFT [9,41], and are dual to marginal operators with dimension ∆ = 4. The expansion (2.17) also has a free integration constant c 1 which corresponds to an operator of dimension ∆ = 6 acquiring an expectation value.…”

“…The supergravity solutions are constructed directly in type IIB supergravity. However, they can also be constructed in an N = 4 D = 5 gauged supergravity theory that can be obtained as a consistent KK truncation of type IIB supergravity on T 1,1 [9][10][11] (extending [12][13][14][15][16][17]). This perspective is helpful in identifying the deformations of the N = 1 SCFT that are needed to flow to the AdS 3 fixed points.…”