The spectral problem of spin chains in N=2 quiver gauge theories

Abstract

We investigate the spectral problem of spin chain models in a family of 4D N =2 superconformal quiver gauge theories, constructed as an orbifold of N = 4 super Yang-Mills theory, in the planar limit. We consider two scalar subsectors, namely, the dense XY sector (constructed out of scalar fields in the bifundamental representation of the gauge groups) and the dilute XZ sector (constructed out of scalar fields in the bifundamental and adjoint representations of the gauge groups). At one-loop level, we show that the XY sector can be mapped to an alternating-bond spin chain model and that the XZ sector can be mapped to a dynamical Temperley-Lieb spin chain model. Using the coordinate Bethe ansatz and techniques from alternating-bond spin chains, we are able to solve the eigenvalue problem for both sectors up to the two magnon level by enhancing the usual Bethe wavefunctions with an extra set of momenta that is not a permutation of the original set of momenta. Thus, the two magnon sector already exhibits diffractive scattering. The solutions exhibit rich physics and properties, such as two scattering matrices and a ratio function, which we study in detail. The dispersion relation, which is shared by both scalar subsectors, can be naturally parametrised using elliptic functions. Finally, given our solution for the two magnon problem, we discuss the challenges that arise in attempting to extend the construction of the wavefunctions to the three magnon problem, as well as the notion of quantum integrability within our scalar subsectors.