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

## TL;DR

This paper proves the integrability of a two-loop open spin chain Hamiltonian in ABJM theory by constructing R- and K-matrices, deriving transfer matrices, and formulating Bethe ansatz equations, advancing understanding of integrable structures in gauge theories.

## Contribution

It explicitly constructs R- and K-matrices for the two-loop ABJM open spin chain, establishing its integrability and deriving Bethe ansatz equations for excited states.

## Key findings

- Successfully constructs R- and K-matrices for the model
- Derives the two-loop Hamiltonian from transfer matrices
- Proposes conjecture for transfer matrix eigenvalues in excited states

## 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.