A Monopole Index for N=4 Chern-Simons Theories

TL;DR

This paper calculates a monopole index for N=4 Chern-Simons theories with gauge group U(N)^r, compares it to the M-theory dual, and confirms their agreement for many sectors, revealing insights into gauge/gravity correspondence.

Contribution

It introduces a new monopole index for N=4 Chern-Simons theories and establishes a detailed correspondence with M-theory dual indices, including wrapped M2-brane contributions.

Findings

Confirmed index agreement for many sectors using analytic methods

Established one-to-one mapping of magnetic charges and dual geometry charges

Highlighted the role of wrapped M2-branes in the index correspondence

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.