On spin chains and field theories

We point out that the existence of global symmetries in a field theory is notan essential ingredient in its relation with an integrable model. We describean obvious construction which, given an integrable spin chain, yields a fieldtheory whose 1-loop scale transformations are generated by the spin chainHamiltonian. We also identify a necessary condition for a given field theory tobe related to an integrable spin chain. As an example, we describe an anisotropic and parity-breaking generalizationof the XXZ Heisenberg spin chain and its associated field theory. The systemhas no nonabelian global symmetries and generally does not admit asupersymmetric extension without the introduction of more propagating bosonicfields. For the case of a 2-state chain we find the spectrum and theeigenstates. For certain values of its coupling constants the field theoryassociated to this general type of chain is the bosonic sector of theLeigh-Strassler deformation of N=4 SYM theory.Comment: 22 pages, Latex; v2. typos correcte