Journal of High Energy Physics, 1903 (2019) 193

Two-loop integrability of ABJM open spin chain from giant graviton

Nan Bai,¹ Hui-Huang Chen,² Hao Ouyang ³ and Jun-Bao Wu ^{4, 5,*}

1. Department of Physics, Guangxi Normal University, Guilin, China

2. College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang, China

3. Nordita, KTH Royal Institute of Technology and Stockholm University, Stockholm, Sweden

4. Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University Tianjin, China

5. Center for High Energy Physics, Peking University, Beijing, China

Abstract

We prove the integrability of the two-loop open spin chain Hamiltonian from ABJM determinant like operators given in ^[1]. 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.