Note on Integrability of Marginally Deformed ABJ(M) Theories
Abstract
We study the anomalous dimensions of operators in the scalar sector of \beta-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 -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 -deformation of ABJ(M) theories and find that the corresponding Hamiltonian is the same as the one in \beta-deformed case at two-loop level in the scalar sector.
Keywords
Cite
@article{arxiv.1302.2208,
title = {Note on Integrability of Marginally Deformed ABJ(M) Theories},
author = {Song He and Jun-Bao Wu},
journal= {arXiv preprint arXiv:1302.2208},
year = {2021}
}
Comments
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