Two-Loop Integrability of ABJM Open Spin Chain from Giant Graviton

Abstract

We prove the integrability of the two-loop open spin chain Hamiltonian from ABJM determinant like operators given in arXiv:1809.09941. By explicitly constructing R-matrices and K-matrices, we successfully obtain the two-loop Hamiltonian from the double row transfer matrices. This proves the integrability of our two-loop Hamiltonian. Based on the vacuum eigenvalues of the transfer matrices, we make a conjecture on the eigenvalues of the transfer matrices for general excited states. Bethe ansatz equations are simply obtained from the analytic conditions at the superficial poles of the eigenvalues.

v3, appendix B added, notation for indices of R and K matrices unified, typoes fixed, published version, 22 pages; v2, 21 pages, no figures, typoes fixed, minor changes

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