Integrable Open Spin Chains in Defect Conformal Field Theory

TL;DR

This paper shows that a specific defect conformal field theory's one-loop scalar sector can be described by an integrable open spin chain, connecting field theory boundary conditions with integrable models.

Contribution

It establishes the integrability of the scalar sector in a defect N=4 SYM perturbation and derives boundary conditions from the spin chain perspective.

Findings

The one-loop dilatation generator matches an integrable open spin chain Hamiltonian.

A K-matrix satisfying the boundary Yang-Baxter equation is constructed.

Dirichlet and Neumann boundary conditions are derived from the field theory.

Abstract

We demonstrate that the one-loop dilatation generator for the scalar sector of a certain perturbation of N=4 Super Yang-Mills with fundamentals is the Hamiltonian of an integrable spin chain with open boundary conditions. The theory is a supersymmetric defect conformal field theory (dCFT) with the fundamentals in hypermultiplets confined to a codimension one defect. We obtain a K-matrix satisfying a suitably generalized form of the boundary Yang-Baxter equation, study the Bethe ansatz equations and demonstrate how Dirichlet and Neumann boundary conditions arise in field theory, and match to existing results in the plane wave limit.