A Monopole Index for N=4 Chern-Simons Theories

Details A Monopole Index for N=4 Chern-Simons Theories A Monopole Index for N=4 Chern-Simons Theories

2009-08-07

arxiv.org/abs/0908.0988v2

Nucl.Phys.B827:183-216,2010

Physics

High Energy Physics

High Energy Physics - Theory

35 pages, v2: typos corrected, a reference added

Scientific paper

10.1016/j.nuclphysb.2009.10.025

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.

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