On spin chains and field theories

Abstract

We point out that the existence of global symmetries in a fleld theory is not an essential ingredient in its relation with an integrable model. We describe an obvious construction which, given an integrable spin chain, yields a fleld theory whose 1-loop scale transformations are generated by the spin chain hamiltonian. We also identify a necessary condition for a given fleld theory to be related to an integrable spin chain. As an example, we describe an anisotropic and parity-breaking generalization of the XXZ Heisenberg spin chain and its associated fleld theory. The system has no nonabelian global symmetries and generally does not admit a supersymmetric extension without the intro- duction of more propagating bosonic flelds. For the case of a 2-state chain we flnd the spectrum and the eigenstates. For certain values of its coupling constants the fleld theory associated to this general type of chain is the bosonic sector of the q-deformation ofN = 4 SYM theory.