The continuum limit of gl(M|N) spin chains

We study the spectrum of an integrable antiferromagnetic Hamiltonian of the gl(M|N) spin chain of alternating fundamental and dual representations. After extensive numerical analysis, we identify the vacuum and low lying excitations and with this knowledge perform the continuum limit, while keeping a finite gap. All antiferromagnetic gl(n+N|N) spin chains with n, N > 0 are shown to possess in the continuum limit 2n - 2 multiplets of massive particles which scatter with gl(n) Gross-Neveu like S-matrices, meaning that their eigenvalues do not depend on N. We argue that the continuum theory is the gl(M|N) Gross-Neveu model, that is the massive deformation of the <(sl)over cap>(M|N)(1) Wess-Zumino-Witten model. As we can see in the example of gl(2m|1) spin chains, the full particle spectrum is much richer. Our analysis suggests that for a complete characterization of the latter it is not enough to restrict to large volume calculations, as we do in this work.