Note on Integrability of Marginally Deformed ABJ(M) Theories

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 $\beta$-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 $\gamma$-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.

22 pages, 7 figures. An term in eq. (3.12) was deleted. After the paper was published in JHEP, We corrected some errors especially the ones in the action of $\beta$-deformed ABJM theory in the e-print on arXiv. Main conclusion and results are unchanged

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Cited by in corpus (7)

• Open Spin Chains from Determinant Like Operators in ABJM Theory
• Integrable Open Spin Chains from Flavored ABJM Theory
• Y-system for $\gamma$-deformed ABJM Theory
• Integrability of Orbifold ABJM Theories
• Loop Operators in Three-Dimensional $\mathcal{N}=2$ Fishnet Theories
• Spectral curve for gamma-deformed AdS/CFT
• T-duality to Scattering Amplitude and Wilson Loop in Non-commutative Super Yang-Mills Theory