Fermion Mass Generation without Spontaneous Symmetry Breaking?
Venkitesh Ayyar
Massless fermions can become massive due to interactions through the mechanism of Spontaneous
Symmetry Breaking (SSB). This mode of mass generation is popular and has been used in the Standard
Model. Here, we explore the possibility of fermions acquiring a mass through interactions, but without
SSB.
We consider a fermion system on a cubical lattice and introduce an on-site four-fermion interaction with
coupling constant U. Using the symmetries of the system on the lattice, we can predict the existence
of massless fermions for small U. For very large values of U, we can argue that the fermions become
massive without the formation of a fermion bilinear condensate. Further, correlation functions seem to
decay exponentially. This suggests that at large U there is a massive fermion phase without SSB.
Monte Carlo results suggest that this phenomenon extends to weaker couplings all the way until the
phase transition to the massless fermion phase. If this transition is second order, then we can take
the continuum limit of the lattice model and obtain an interesting Quantum Field Theory with a new
mechanism for fermion mass generation.
Venkitesh received a laser pointer with his talk.
