The complete superconformal index for N=6N=6 Chern–Simons theory

We calculate the superconformal index for N=6N=6 Chern–Simons-matter theory with gauge group U(N)k×U(N)−kU(N)k×U(N)−k at arbitrary allowed value of the Chern–Simons level k  . The calculation is based on localization of the path integral for the index. Our index counts supersymmetric gauge invariant operators containing inclusions of magnetic monopole operators, where latter operators create magnetic fluxes on 2-sphere. Through analytic and numerical calculations in various sectors, we show that our result perfectly agrees with the index over supersymmetric gravitons in AdS4×S7/ZkAdS4×S7/Zk in the large N   limit. Monopole operators in nontrivial representations of U(N)×U(N)U(N)×U(N) play important roles. We also comment on possible applications of our methods to other superconformal Chern–Simons theories.