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Note on integrability of marginally deformed ABJ(M) theories

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An Erratum to this article was published on 21 April 2016

Abstract

We study the anomalous dimensions of operators in the scalar sector of β-deformed ABJ(M) theories. We show that the anomalous dimension matrix at two-loop order gives an integrable Hamiltonian acting on an alternating SU(4) spin chain with the spins at odd lattice sides in the fundamental representation and the spins at even lattices in the anti-fundamental representation. We get a set of β-deformed Bethe ansatz equations which give the eigenvalues of Hamiltonian of this deformed spin chain system. Based on our computations, we also extend our study to non-supersymmetric three-parameter γ-deformation of ABJ(M) theories and find that the corresponding Hamiltonian is the same as the one in β-deformed case at two-loop level in the scalar sector.

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Authors and Affiliations

  1. State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Science, No. 55 Zhongguancun East Road, Beijing, 100190, P.R. China

    Song He

  2. Kavli Institute for Theoretical Physics China, CAS, No. 55 Zhongguancun East Road, Beijing, 100190, P.R. China

    Song He

  3. Institute of High Energy Physics and Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences, 19B YuquanLu, Beijing, 100049, P.R. China

    Jun-Bao Wu

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ArXiv ePrint: 1302.2208

An erratum to this article can be found at http://dx.doi.org/10.1007/JHEP04(2016)139.

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He, S., Wu, JB. Note on integrability of marginally deformed ABJ(M) theories. J. High Energ. Phys. 2013, 12 (2013). https://doi.org/10.1007/JHEP04(2013)012

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