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.

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

References in corpus (10)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
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• Integrable Spin Chain in Superconformal Chern-Simons Theory
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• Quasilocality of joining/splitting strings from coherent states

Cited by in corpus (4)

• Anomalous radius shift in AdS(4)/CFT(3)
• Non-planar ABJ Theory and Parity
• The Morphology of N=6 Chern-Simons Theory
• Semiclassical strings in AdS(3) X S^2