Self-consistency of conformally coupled ABJM theory at the quantum level

Abstract

Abstract We study the $$ \mathcal{N} $$ N = 6 superconformal Chern-Simons matter field theory (the ABJM theory) conformally coupled to a Lorentzian, curved background spacetime. To support rigid supersymmetry, such backgrounds have to admit twistor spinors. At the classical level, the symmetry of the theory can be described by a conformal symmetry superalgebra. We show that the full $$ \mathcal{N} $$ N = 6 superconformal algebra persists at the quantum level using the BV-BRST method.