Stability and boundedness in AdS/CFT with double trace deformations II: Vector Fields

We extend the analysis of boundedness and stability, initiated for scalar fields in anti de Sitter space in a previous work, to the case of vector fields. We show that the double trace deformation of Marolf and Ross is distinct from the double trace deformation of Witten. The former gives rise to an $SL(2,\mathbf{R})$ family of theories whereas the latter gives rise to an independent $SL(2,\mathbf{Z})$. We analyze the finite temperature two-point correlation function of current operators and infer the susceptibility and spectrum of low lying states. We discuss various physical features exhibited by these theories.