Exact results on ABJ theory and the refined topological string

We study the partition function of the ABJ theory, which is the N = 6 superconformal Chern-Simons matter theory with gauge group U(N) x U(N + M) and Chern-Simons levels (k, -k). We exactly compute the ABJ partition function on a three sphere for various k, M and N via the Fermi gas approach. By using these exact data, we show that the ABJ partition function is completely determined by the refined topological string on local P-1 x P-1, including membrane instanton effects in the M-theory dual.ArticleJOURNAL OF HIGH ENERGY PHYSICS. 2014(8):148 (2014)journal articl