Integrability of Orbifold ABJM Theories

TL;DR

This paper demonstrates that the integrable structure of planar ABJM theories persists after orbifolding by discrete groups, providing explicit Bethe ansatz equations and eigenvalues for various orbifold cases.

Contribution

It proves integrability in the scalar sector at two loops for general orbifolds and proposes all-sector and all-loop Bethe ansatz equations for supersymmetric orbifolds.

Findings

Integrability survives orbifolding with discrete groups.

Explicit Bethe ansatz equations are derived for various orbifolds.

Eigenvalues of anomalous dimension matrices are obtained.

Abstract

Integrable structure has played a very important role in the study of various non-perturbative aspects of planar ABJM theories. In this paper we showed that this remarkable structure survive after orbifold operation with discrete group $\Gamma(\simeq\mathbb{Z}_n)<SU(4)_R\times U(1)_b$. For general $\Gamma$, we prove the integrability in the scalar sector at the planar two-loop order and get the Bethe ansatz equations. The eigenvalues of the anomalous dimension matrix are also obtained. For $\Gamma<SU(4)$, two-loop all-sector and all-loop BAEs are proposed. Supersymmetric orbifolds are discussed in this framework.