A Monopole Index for N=4 Chern-Simons Theories

Abstract

We compute a certain index for an N=4 Chern-Simons theory with gauge group U(N)^r in the large N limit with taking account of monopole contribution, and compare it to the corresponding multi-particle index for M-theory in the dual geometry AdS_4 x X_7. The internal space X_7 has non-trivial two-cycles, and M2-branes wrapped on them contribute to the multi-particle index. We establish one-to-one map between r-1 independent magnetic charges on the gauge theory side and the same number of charges on the gravity side: the M-momentum and r-2 (=b_2(X_7)) wrapping numbers. With a certain assumption for the wrapped M2-brane contribution, we confirm the agreement of the indices for many sectors specified by the r-1 charges by using analytic and numerical methods.

35 pages, v2: typos corrected, a reference added

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• Tests of AdS${}_4$/CFT${}_3$ correspondence for $\mathcal{N}=2$ chiral-like theory
• ABCD of 3d $\mathcal{N}=8$ and 4 Superconformal Field Theories
• Twisted Sectors in Gravity Duals of N=4 Chern-Simons Theories
• Probing AdS4/CFT3 proposals beyond chiral rings
• On thermodynamics of N=6 superconformal Chern-Simons theory
• Aspects of ABJM orbifolds
• Index for Three Dimensional Superconformal Field Theories and Its Applications
• BPS solutions in ABJM theory and Maximal Super Yang-Mills on RxS^2
• Cartan-Weyl 3-algebras and the BLG Theory I: Classification of Cartan-Weyl 3-algebras
• Matrix Model of Chern-Simons Matter Theories Beyond The Spherical Limit
• Semi-classical monopole operators in Chern-Simons-matter theories
• Enhanced Supersymmetry of Nonrelativistic ABJM Theory
• Superconformal Index for $\mathcal{N}=3$ $\widehat{ADE}$ Chern-Simons Quiver Gauge Theories