Holographic RG flows and symplectic deformations of N =4 gauged supergravity

We study four-dimensional N =4 gauged supergravity with S O (4 )×S O (4 )∼S O (3 )×S O (3 )×S O (3 )×S O (3 ) gauge group in the presence of symplectic deformations. There are in general four electric-magnetic phases corresponding to each S O (3 ) factor, but two phases of the S O (3 ) factors embedded in the S O (6 ) R-symmetry are fixed. One phase can be set to zero by S L (2 ,R ) transformations. The second one gives equivalent theories for any nonvanishing values and can be set to π/2 resulting in gauged supergravities that admit N =4 supersymmetric AdS₄ vacua. The remaining two phases are truly deformation parameters leading to different S O (4 )×S O (4 ) gauged supergravities. As in the ω -deformed S O (8 ) maximal gauged supergravity, the cosmological constant and scalar masses of the AdS₄ vacuum at the origin of the scalar manifold with S O (4 )×S O (4 ) symmetry do not depend on the electric-magnetic phases. We find N =1 holographic RG flow solutions between N =4 critical points with S O (4 )×S O (4 ) and S O (3 )dia_g×S O (3 )×S O (3 ) or S O (3 )×S O (3 )dia_g×S O (3 ) symmetries. We also give N =2 and N =1 RG flows from these critical points to various nonconformal phases. However, contrary to the ω -deformed S O (8 ) gauged supergravity, there exist nontrivial supersymmetric AdS₄ critical points only for particular values of the deformation parameters within the scalar sectors under consideration.