Non-planar ABJM Theory and Integrability

TL;DR

This paper derives the two-loop dilatation generator of ABJM theory including non-planar corrections and investigates how these affect operator degeneracies and integrability properties.

Contribution

It explicitly computes non-planar corrections to the dilatation generator in ABJM theory and analyzes their impact on operator degeneracies and integrability.

Findings

Planar degeneracy due to integrability is lifted by non-planar corrections.

Non-planar terms vanish in the strict BMN limit for BMN operators.

Degeneracies between parity pairs disappear with non-planar corrections.

Abstract

Using an effective vertex method we explicitly derive the two-loop dilatation generator of ABJM theory in its SU(2)xSU(2) sector, including all non-planar corrections. Subsequently, we apply this generator to a series of finite length operators as well as to two different types of BMN operators. As in N=4 SYM, at the planar level the finite length operators are found to exhibit a degeneracy between certain pairs of operators with opposite parity - a degeneracy which can be attributed to the existence of an extra conserved charge and thus to the integrability of the planar theory. When non-planar corrections are taken into account the degeneracies between parity pairs disappear hinting the absence of higher conserved charges. The analysis of the BMN operators resembles that of N=4 SYM. Additional non-planar terms appear for BMN operators of finite length but once the strict BMN limit is taken these terms disappear.