Observables and correlators in non-relativistic ABJM theory

Abstract

Non-relativistic ABJM theory is defined by Galilean limit of mass-deformed = 6 Chern-Simons theory. Holographic string theory dual to the theory is not known yet. To understand features candidate gravity dual might exhibit, we examine local and nonlocal physical observables and their correlations in the non-relativistic ABJM theory. We show that gauge invariant local observables correspond to zero-norm states and that correlation functions among them are trivial. We also show that a particular class of nonlocal observables, Wilson loops, are topological in the sense that their correlation functions coincide with those of pure Chern-Simons theory. We argue that the theory is nevertheless physical and illustrate several physical observables whose correlation functions are nontrivial. We also study quantum aspects. We show that Chern-Simons level is finitely renormalized and that dilatation operator is trivial at planar limit. These results all point to string scale geometry of gravity dual and to intriguing topological and tensionless nature of dual string or M theory defined on it.