Non-planar ABJM Theory and Integrability

Details Non-planar ABJM Theory and Integrability Non-planar ABJM Theory and Integrability

2008-11-13

arxiv.org/abs/0811.2150v3

JHEP 0903:037,2009

Physics

High Energy Physics

High Energy Physics - Theory

1+26 pages, uses axodraw.sty. v2: typos fixed, references added. v3: more typos fixed, minor corrections

Scientific paper

10.1088/1126-6708/2009/03/037

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.

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