Relating U(N)xU(N) to SU(N)xSU(N) Chern-Simons Membrane theories

Abstract

By integrating out the U(1)_B gauge field, we show that the U(n)xU(n) ABJM theory at level k is equivalent to a Z_k identification of the (SU(n)xSU(n))/Z_n Chern-Simons theory, but only when n and k are coprime. As a consequence, the k=1 ABJM model for two M2-branes in R^8 can be identified with the N=8 (SU(2)xSU(2))/Z_2 theory. We also conjecture that the U(2)xU(2) ABJM model at k=2 is equivalent to the N=8 SU(2)xSU(2)-theory.

16 pages, Latex; v2: references added; v3: Clarifications added

References in corpus (11)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Fractional M2-branes
• Membranes on an Orbifold
• Moduli spaces of Chern-Simons quiver gauge theories and AdS_4/CFT_3
• Studies of the ABJM Theory in a Formulation with Manifest SU(4) R-Symmetry
• On M5-branes in N=6 Membrane Action
• Notes on Supersymmetry Enhancement of ABJM Theory
• Enhanced N=8 Supersymmetry of ABJM Theory on R(8) and R(8)/Z(2)

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• Lessons from M2's and Hopes for M5's
• Dualities and flavored indices of M2-brane SCFTs
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• Dimensional reduction of the ABJM model
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