  We investigate a holographic realization in Type-IIB string theory of pure
Chern-Simons theories, and focus on the level/rank dualities that they enjoy.
The level/rank duality is established between the boundary theory, engineered
utilizing D3-branes compactified on a $S^1$, and the theory on probe D7-branes
located at a specific bulk location. Paying attention to the boundary
conditions imposed on the Ramond-Ramond (RR) two- and six-forms, we show that
holography precisely reproduces several different level/rank dual pairs. The
$SL(2,\mathbf{Z})$ action relating all these theories is realized through the
$SL(2,\mathbf{Z})$ electric/magnetic duality involving the RR potentials.
