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arXiv · 0811.2150

Non-planar ABJM Theory and Integrability

Charlotte Kristjansen·Marta Orselli·Konstantinos Zoubos
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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.

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Charlotte Kristjansen, Marta Orselli, Konstantinos Zoubos. 2009-03-31. Non-planar ABJM Theory and Integrability. https://doi.org/10.1088/1126-6708%2F2009%2F03%2F037

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