$$AdS_5$$ A d S 5 vacua and holographic RG flows from 5D $$N=4$$ N = 4 gauged supergravity

Abstract

Abstract We study five-dimensional $$N=4$$ N = 4 gauged supergravity coupled to five vector multiplets with $$SO(2)_D\times SO(3)\times SO(3)$$ S O ( 2 ) D × S O ( 3 ) × S O ( 3 ) gauge group. There are four supersymmetric $$AdS_5$$ A d S 5 vacua in the truncation to $$SO(2)_{\text {diag}}$$ S O ( 2 ) diag invariant scalars. Two of these vacua preserve the full $$N=4$$ N = 4 supersymmetry with $$SO(2)_D\times SO(3)\times SO(3)$$ S O ( 2 ) D × S O ( 3 ) × S O ( 3 ) and $$SO(2)_D\times SO(3)_{\text {diag}}$$ S O ( 2 ) D × S O ( 3 ) diag symmetries. These have an analogue in $$N=4$$ N = 4 gauged supergravity with $$SO(2)\times SO(3)\times SO(3)$$ S O ( 2 ) × S O ( 3 ) × S O ( 3 ) gauge group. The other two $$AdS_5$$ A d S 5 vacua preserve only $$N=2$$ N = 2 supersymmetry with $$SO(2)_{\text {diag}}\times SO(3)$$ S O ( 2 ) diag × S O ( 3 ) and $$SO(2)_{\text {diag}}$$ S O ( 2 ) diag symmetry. The former has an analogue in the previous study of $$SO(2)_D\times SO(3)$$ S O ( 2 ) D × S O ( 3 ) gauge group while the latter is a genuinely new $$N=2$$ N = 2 $$AdS_5$$ A d S 5 vacuum. These vacua should be dual to $$N=2$$ N = 2 and $$N=1$$ N = 1 superconformal field theories (SCFTs) in four dimensions with different flavour symmetries. We give the full scalar mass spectra at all of the $$AdS_5$$ A d S 5 critical points which provide information on conformal dimensions of the dual operators. Finally, we study holographic RG flows interpolating between these $$AdS_5$$ A d S 5 vacua and find a new class of solutions. In addition to the RG flows from the trivial $$SO(2)_D\times SO(3)\times SO(3)$$ S O ( 2 ) D × S O ( 3 ) × S O ( 3 ) $$N=4$$ N = 4 critical point, at the origin of the scalar manifold, to all the other critical points, there is a family of RG flows from the trivial $$N=4$$ N = 4 critical point to the new $$SO(2)_{\text {diag}}$$ S O ( 2 ) diag $$N=2$$ N = 2 critical point that pass arbitrarily close to the $$SO(2)_D\times SO(3)_{\text {diag}}$$ S O ( 2 ) D × S O ( 3 ) diag $$N=4$$ N = 4 critical point.