  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 $SL(2,{\bf R})$ family of theories whereas the latter gives rise to an
independent $SL(2,{\bf Z})$. 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.
