The Bethe ansatz for superconformal Chern-Simons

By J. Minahan, K. Zarembo. 2008

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We study the anomalous dimensions for scalar operators for a three-dimensional Chern-Simons theory recently proposed in arXiv:0806.1218. We show that the mixing matrix at two-loop order is that for an integrable Hamiltonian of an SU(4) spin chain with sites alternating between the fundamental and the anti-fundamental representations. We find a set of Bethe equations from which the anomalous dimensions can be determined and give a proposal for the Bethe equations to the full superconformal group of OSp(2,2|6).

Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b1a5874ffa4a015d38f6c633d4d2277927b99df6

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Citations in the corpus

N = 6 super Chern-Simons theory S-matrix and all-loop Bethe ansatz equations (2008, background): “) The integrability of the planar N = 6 CS was first discovered by Minahan and Zarembo [8] in the leading two-loop-order perturbative computation of the anomalous dimensions of gauge-invariant composite operators.”
Three-dimensional N=6 SCFT's and their membrane dynamics (2008, methodology): “A notable feature of the string theory limit of the ABJM theory, whose sigma model was studied in [14, 15] and, using a covariant formulation, in [16], is that it appears to be integrable [17, 18] (see also [19, 20]).”
Spinning strings at one-loop in AdS(4) x P**3 (2008, methodology): “The dilatation operator of the N = 6 Chern-Simons theory was shown [16, 18], to leading order in the scalar sector, to be equivalent to the Hamiltonian of an integrable (alternating) spin chain.”
Anomalous radius shift in AdS4/CFT3 (2009, background): “At large N and k the theory has an ’tHooft (planar) limit with fixed λ ≡ N/k, and the field theory description is (perturbatively) valid when λ≪ 1, i.e. for k ≫ N .”
Semiclassical quantization of spinning strings in AdS4 × ℂℙ3 (2008, background): “Complementary, the planar superconformal Chern-Simons theory appears to be integrable at leading order in the weak coupling expansion [8, 9, 10].”
Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal (2008, background): “This is for a good reason, as both the perturbative gauge theory and the dual free string theory appear to be integrable (as was partially verified at two-loop level in gauge theory – namely in the scalar sector [2] – and at the classical level in string theory [3, 4]).”
Towards integrability for AdS 3 / CFT 2 ?> (2014, background): “Integrability manifests itself in the ABJM theory, where an integrable spin-chain Hamiltonian was found first at two loop in perturbation theory [143, 144].”
Spin Chains in N = 6 Superconformal Chern-Simons-Matter Theory (2008, methodology): “Note added in proof: Upon completion of the bulk of this work, we received [19] and [16], which contain results that overlap with different parts of this paper.”
Superstrings on AdS4 × ℂℙ3 as a coset sigma-model (2008, background): “in the weak coupling expansion the corresponding dilatation operator can be identified with an integrable Hamiltonian of the SU(4) spin chain with spins alternating between fundamental and anti-fundamental representations [4].”
N=5,6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds (2008, background): “The relevant topics include extension to N = 4 orbifolds [27, 28], superconformal indices [29], Penrose limit [30], integrability [31], non-supersymmetric generalization [32], and partition function [16].”
Integrability, spin-chains and the AdS3/CFT2 correspondence (2011, positive): “Restricting to just one osp(4|2) factor the spin-chain we construct is closely related to the ABJM spin-chain constructed in [57].”