Two Phase Transitions in Chiral Gross-Neveu Model in $2+ \epsilon$ Dimensions at Low N

TL;DR

This paper investigates the chiral Gross-Neveu model in slightly above two dimensions, revealing two distinct phase transitions at low fermion number: one for pair formation and another for pair condensation leading to chiral symmetry breaking.

Contribution

It demonstrates the existence of two separate phase transitions in the model, providing insights into mass generation and chiral symmetry breaking mechanisms.

Findings

Fermions form bound pairs with a mass in the first transition.

Bose liquid of pairs condenses, breaking chiral symmetry in the second transition.

Two phase transitions occur at low N in the model.

Abstract

We show that the chiral Gross-Neveu model in $2+ \epsilon$ dimensions has for a small number $N$ of fermions two phase transitions corresponding to pair formation and pair condensation. In the first transition, fermions and antifermions acquire spontaneously a mass and are bound to pairs which behave like a Bose liquid in a chirally symmetric state. In the second transition, the Bose liquid condenses into a coherent state which breaks chiral symmetry. This suggests the possibility that in particle physics, the generation of quark masses may also happen separately from the breakdown of chiral symmetry.