Comments on Holographic Level/Rank Dualities

Abstract

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, Z) action relating all these theories is realized through the SL(2, Z) electric/magnetic duality involving the RR potentials.