Nonplanar Integrability and Parity in ABJ 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.

1+12 pages, Corrected typos, more clarifications, figure and appendix added

References in corpus (8)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Spin Chains in N=6 Superconformal Chern-Simons-Matter Theory
• Diagonal multi-matrix correlators and BPS operators in N=4 SYM
• Branes, Anti-Branes and Brauer Algebras in Gauge-Gravity duality
• Two loop integrability for Chern-Simons theories with N=6 supersymmetry
• Nonplanar Integrability
• Surprisingly Simple Spectra
• Non-planar ABJ Theory and Parity