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

25 pages

References in corpus (7)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• Level/rank Duality and Chern-Simons-Matter Theories
• Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States, and Hierarchy
• Generalized symmetries and holography in ABJM-type theories
• Embedding three-dimensional bosonization dualities into string theory
• Vacuum structure of large $N$ QCD${}_3$ from holography

Cited by in corpus (1)

• Continuous Generalized Symmetries in Three Dimensions