Abstract
We study four-dimensional N=4 gauged supergravity coupled to six vector multiplets with semisimple gauge groups SO(4)times SO(4), SO(3,1)times SO(3,1) and SO(4)times SO(3,1). All of these gauge groups are dyonically embedded in the global symmetry group SO(6, 6) via its maximal subgroup SO(3,3)times SO(3,3). For SO(4)times SO(4) gauge group, there are four N=4 supersymmetric AdS_4 vacua with SO(4)times SO(4), SO(4)times SO(3), SO(3)times SO(4) and SO(3)times SO(3) symmetries, respectively. These AdS_4 vacua correspond to N=4 SCFTs in three dimensions with SO(4) R-symmetry and different flavor symmetries. We explicitly compute the full scalar mass spectra at all these vacua. Holographic RG flows interpolating between these conformal fixed points are also given. The solutions describe supersymmetric deformations of N=4 SCFTs by relevant operators of dimensions Delta =1,2. A number of these solutions can be found analytically although some of them can only be obtained numerically. These results provide a rich and novel class of N=4 fixed points in three-dimensional Chern–Simons-Matter theories and possible RG flows between them in the framework of N=4 gauged supergravity in four dimensions. Similar studies are carried out for non-compact gauge groups, but the SO(4)times SO(4) gauge group exhibits a much richer structure.
Highlights
Rather than finding holographic RG flow solutions directly in string/M-theory, a convenient and effective way to find these solutions is to look for domain wall solutions in lower dimensional gauged supergravities
Possible gauge groups are embedded in the global symmetry group S L(2, R) × S O(6, 6)
We have studied dyonic gaugings of N = 4 supergravity coupled to six vector multiplets with compact and non-compact gauge groups S O(4) × S O(4), S O(3, 1) × S O(3, 1) and S O(4) × S O(3, 1)
Summary
Rather than finding holographic RG flow solutions directly in string/M-theory, a convenient and effective way to find these solutions is to look for domain wall solutions in lower dimensional gauged supergravities. Solutions in the case of non-semisimple gauge groups with known higher dimensional origins have already been considered in [19,20]. We are interested in N = 4 gauged supergravity coupled to six vector multiplets to simplify the computation In this case, possible gauge groups are embedded in the global symmetry group S L(2, R) × S O(6, 6). 2, we review N = 4 gauged supergravity coupled to vector multiplets in the embedding tensor formalism. This sets up the framework we will use throughout the paper and collects relevant formulae and notations used in subsequent sections. The scalar potential is given in terms of the scalar coset representative and the embedding tensor by
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