Observables and Correlators in Nonrelativistic ABJM Theory

TL;DR

This paper investigates the non-relativistic ABJM theory by analyzing local and nonlocal observables, revealing its topological features, trivial local correlations, and implications for potential gravity duals.

Contribution

It provides a detailed analysis of physical observables in non-relativistic ABJM theory, highlighting their topological nature and quantum properties, and discusses implications for holographic duals.

Findings

Gauge invariant local observables have zero norm and trivial correlations.

Wilson loops are topological, matching pure Chern-Simons theory.

Chern-Simons level is finitely renormalized, and the dilatation operator is trivial at planar limit.

Abstract

Non-relativistic ABJM theory is defined by Galilean limit of mass-deformed N=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 acting on spin chain 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 defined on it.