Integrable Open Spin Chains in Defect Conformal Field Theory

TL;DR

The paper demonstrates that the planar one-loop dilatation operator for a defect conformal field theory with fundamentals coincides with the Hamiltonian of an integrable open spin chain, including a boundary K-matrix solution to a generalized boundary Yang-Baxter equation. By constructing the open-chain transfer matrix with explicit K^- and K^+ matrices, the authors confirm integrability and derive Bethe Ansatz equations for single-impurity excitations, finding Dirichlet or Neumann boundary conditions that align with open-string boundary behavior. The plane-wave limit analysis shows agreement with the string-theory results of the dual AdS/dCFT setup, via a doubling trick that relates open-string excitations to closed-chain modes. Overall, the work extends integrability from N=4 SYM to a defect theory with fundamental matter, offering a bridge between open-string boundary conditions and field-theoretic spin chains and suggesting avenues to explore open-string Yangian symmetries in the holographic dual.

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.