Integrable Spin Chain and Operator Mixing in N=1,2 Supersymmetric Theories

TL;DR

This paper demonstrates that operator mixing in certain supersymmetric theories can be described by integrable quantum spin chains, revealing a universal integrable structure beyond superconformal symmetry and highlighting the superpotential's role.

Contribution

It identifies integrable spin chain Hamiltonians in N=1,2 supersymmetric models' operator mixing, extending the understanding of integrability beyond superconformal theories.

Findings

Operator mixing maps to SU(3) or SU(2) spin chains.

Integrable structure persists away from conformal points.

New features in Bethe Ansatz solutions compared to N=4 SYM.

Abstract

We study operator mixing, due to planar one-loop corrections, for composite operators in D=4 supersymmetric theories. We present some N=1,2 Yang-Mills and Wess-Zumino models, in which the planar one-loop anomalous dimension matrix in the sector of holomorphic scalars is identified with the Hamiltonian of an integrable quantum spin chain of SU(3) or SU(2) symmetry, even if the theory is away from the conformal points. This points to a more universal origin of the integrable structure beyond superconformal symmetry. We also emphasize the role of the superpotential in the appearance of the integrable structure. The computations of operator mixing in our examples by solving Bethe Ansatz equations show some new features absent in N=4 SYM.