Non-planar ABJM Theory and Integrability
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.
Cite
@article{arxiv.0811.2150,
title = {Non-planar ABJM Theory and Integrability},
author = {Charlotte Kristjansen and Marta Orselli and Konstantinos Zoubos},
journal= {arXiv preprint arXiv:0811.2150},
year = {2009}
}
Comments
1+26 pages, uses axodraw.sty. v2: typos fixed, references added. v3: more typos fixed, minor corrections