On the phase structure of a chiral invariant Higgs-Yukawa model

In the past the construction of Higgs-Yukawa models on the lattice was blocked by the lack of a consistent definition of a chiral invariant Yukawa coupling term. Here, we consider a chiral invariant Higgs-Yukawa model based on the overlap operator, realized by the Neuberger-Dirac operator. As a first step towards a numerical examination of this model we study its phase diagram by means of an analytic 1/N-expansion, which is possible for small and for large values of the Yukawa coupling constant. In the case of strong Yukawa couplings the model effectively becomes an O(4)-symmetric non-linear sigma-model.