Nonplanar Integrability and Parity in ABJ Theory

TL;DR

This paper investigates the non-planar two-loop dilatation operator in ABJ theory, revealing integrability in a specific limit and examining how parity symmetry is broken or restored depending on the parameters, thus connecting gauge theory and string duality.

Contribution

It demonstrates integrability in the large M and N double limit of ABJ theory and explores parity symmetry breaking and restoration in relation to the theory's parameters.

Findings

Spectrum reduces to decoupled harmonic oscillators in a certain limit.

Parity invariance is broken by non-planar anomalous dimensions.

Parity is restored when ABJ reduces to ABJM theory.

Abstract

In this article we study the action of the non-planar two-loop dilatation operator in an SU(2)*SU(2) sub-sector of the ABJ Chern-Simons-matter theory. The gauge invariant operators we consider are the restricted Schur polynomials. As in ABJM theory, there is a limit in which the spectrum reduces to a set of decoupled harmonic oscillators, indicating integrability in the large M and N double limit of the theory. We then consider parity transformations on the gauge invariant operators. In this case the non-planar anomalous dimensions break parity invariance. Our analysis shows that (M-N) is related to the holonomy in the string theory, confirming one of the main features of the theory and its string dual. Furthermore, in the limit where ABJ theory reduces to ABJM theory, parity invariance is restored.