Two-Dimensional Non-Linear Sigma Models as a Limit of the Linear Sigma Models

  title={Two-Dimensional Non-Linear Sigma Models as a Limit of the Linear Sigma Models},
  author={H. Sonoda},
  journal={Progress of Theoretical Physics},
  • H. Sonoda
  • Published 3 August 2004
  • Mathematics, Physics
  • Progress of Theoretical Physics
We show how to obtain the O(N) non-linear sigma model in two dimensions as a strong coupling limit of the corresponding linear sigma model. In taking the strong coupling limit, the squared mass parameter must be given a specific coupling dependence that assures the finiteness of the physical mass scale. The relation discussed in this paper, which applies to the renormalized theories as opposed to the regularized theories, is possibly an example of a general relation between the linear and non… 

Figures from this paper



Statistical Field Theory

Classical equilibrium statistical mechanics magnetic systems the Ising model the low-temperature and high-temperature expansions the Landau-Ginsberg model near the transition the renormalization


  • Repts. 12C, 75
  • 1974


  • Lett. B280, 75
  • 1991

Note that the renormalized coupling constant g and renormalized field Φ I are chosen such that the two-loop beta function g 2 + cg 3 and the one-loop anomalous dimension γg become exact

    Here r is an arbitrary vector, hence re t is not necessarily integral. If t is big enough, we can always approximate re t by an integral vector


      • Rev. D10, 3235
      • 1974


      • Lett. B153, 297
      • 1985


      • Phys. B365, 79
      • 1991

      The first three papers show the equivalence of a four-Fermi theory with a Yukawa theory. The reason for this equivalence is the same as for that between the O(N ) linear and non-linear sigma models

        The Boltzmann weight is given by e S