ABJ theory in the higher spin limit

A bstract We study the conjecture made by Chang, Minwalla, Sharma, and Yin on the duality between the N = 6 Vasiliev higher spin theory on AdS 4 and the N = 6 Chern-Simons-matter theory, so-called ABJ theory, with gauge group U( N ) × U( N + M ). Building on our earlier results on the ABJ partition function, we develop the systematic 1 /M expansion, corresponding to the weak coupling expansion in the higher spin theory, and compare the leading 1 /M correction, with our proposed prescription, to the one-loop free energy of the N = 6 Vasiliev theory. We find an agreement between the two sides up to an ambiguity that appears in the bulk one-loop calculation.