ABJ Theory in the Higher Spin Limit

TL;DR

This paper investigates the duality between a higher spin gravity theory in AdS_4 and a specific Chern-Simons-matter theory, developing a 1/M expansion and comparing free energies to support the conjecture.

Contribution

It provides a systematic 1/M expansion of the ABJ theory and compares the leading correction to the one-loop free energy in the higher spin dual, offering evidence for the duality.

Findings

Agreement between bulk one-loop free energy and boundary theory up to an ambiguity.

Development of a systematic 1/M expansion for ABJ partition function.

Support for the conjectured duality between ABJ theory and higher spin gravity.

Abstract

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) x 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.