A New Method for Studying Supersymmetric Chern-Simons-matter Theories

ABJM theory as a Fermi gas

We develop a new method to study the partition function on the three-sphere of many supersymmetric chern-simons-matter theories in the m-theory limit, but at all orders in the 1/n expansion.The method is based on reformulating the matrixmodel as the partition function of an ideal fermi gas with a non-trivial, one-particle quantum hamiltonian.This new approach leads to a completelyelementary derivation of the n^{3/2} behavior for the partition function on the three-sphere of many supersymmetric chern-simons-matter theories.In addition, the full series of 1/n corrections to the original matrix integral can be simply determined by a next-to-leading calculation in the semiclassical expansion of the quantum gas, and we show that, for several quiver chern-simons-matter theories, it is given by an airy function.