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

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Cited by in corpus (31)

• Summing Up All Genus Free Energy of ABJM Matrix Model
• Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant
• Review of AdS/CFT Integrability, Chapter IV.3: N=6 Chern-Simons and Strings on AdS4xCP3
• Anomalous radius shift in AdS(4)/CFT(3)
• Simplifying superstring and D-brane actions in AdS(4) x CP(3) superbackground
• Magnon dispersion to four loops in the ABJM and ABJ models
• Y-system, TBA and Quasi-Classical Strings in AdS4 x CP3
• Two-loop Integrability of Planar N=6 Superconformal Chern-Simons Theory
• Infrared Stability of N=2 Chern-Simons Matter Theories
• Review of AdS/CFT Integrability, Chapter IV.1: Aspects of Non-Planarity
• Non-planar ABJ Theory and Parity
• Finite-size corrections for quantum strings on AdS_4 x CP^3
• Full Lagrangian and Hamiltonian for quantum strings on AdS_4 x CP^3 in a near plane wave limit
• Integrability of N=6 Chern-Simons Theory at Six Loops and Beyond
• Beyond the Planar Limit in ABJM
• Strings in AdS_4 x CP^3: finite size spectrum vs. Bethe Ansatz
• On the spectral problem of N=4 SYM with orthogonal or symplectic gauge group
• On the worldsheet theory of the type IIA AdS(4) x CP(3) superstring
• The Morphology of N=6 Chern-Simons Theory
• Hints of Integrability Beyond the Planar Limit: Nontrivial Backgrounds
• Two-Loop Spectroscopy of Short ABJM Operators
• Open Spin Chains from Determinant Like Operators in ABJM Theory
• Note on Integrability of Marginally Deformed ABJ(M) Theories
• New Penrose Limits and AdS/CFT
• Spin chain for the deformed ABJM theory
• On thermodynamics of N=6 superconformal Chern-Simons theory
• On the absence of reflection in AdS4/CFT3
• Semiclassical strings in AdS(3) X S^2
• Heavy Operators in Superconformal Chern-Simons Theory
• Multi-Spin Strings in AdS_4*CP^3 and its β-deformation
• Splitting of Folded Strings in AdS_4*CP^3