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Fermion mass without symmetry breaking

Simon Catterall

TL;DR

The paper investigates a three-dimensional lattice model of reduced staggered fermions with an $SO(4)$-invariant four-fermion interaction, showing that a mass gap can emerge at strong coupling without forming a bilinear condensate, and that the transition from the massless to the massive phase appears continuous. Using an auxiliary-field reformulation, the authors argue that the usual Gross–Neveu mechanism for symmetry breaking is unlikely and that the mass generation arises from a symmetric four-fermion condensate. Numerical simulations reveal a two-phase structure (massless PMW and massive PMS) separated by a continuous transition near $G_c$, with no evidence of intermediate symmetry-breaking phases. The work highlights a novel mass-generation mechanism without symmetry breaking and motivates exploration of continuum limits, potential extension to four dimensions, and connections to condensed-matter systems exhibiting symmetry-protected mass gaps.

Abstract

We examine a model of reduced staggered fermions in three dimensions interacting through an $SO(4)$ invariant four fermion interaction. The model is similar to that considered in a recent paper by Ayyer and Chandrasekharan \cite{Ayyar:2014eua}. We present theoretical arguments and numerical evidence which support the idea that the system develops a mass gap for sufficiently strong four fermi coupling.{\it without} producing a symmetry breaking fermion bilinear condensate. Massless and massive phases appear to be separated by a continuous phase transition.

Fermion mass without symmetry breaking

TL;DR

The paper investigates a three-dimensional lattice model of reduced staggered fermions with an -invariant four-fermion interaction, showing that a mass gap can emerge at strong coupling without forming a bilinear condensate, and that the transition from the massless to the massive phase appears continuous. Using an auxiliary-field reformulation, the authors argue that the usual Gross–Neveu mechanism for symmetry breaking is unlikely and that the mass generation arises from a symmetric four-fermion condensate. Numerical simulations reveal a two-phase structure (massless PMW and massive PMS) separated by a continuous transition near , with no evidence of intermediate symmetry-breaking phases. The work highlights a novel mass-generation mechanism without symmetry breaking and motivates exploration of continuum limits, potential extension to four dimensions, and connections to condensed-matter systems exhibiting symmetry-protected mass gaps.

Abstract

We examine a model of reduced staggered fermions in three dimensions interacting through an invariant four fermion interaction. The model is similar to that considered in a recent paper by Ayyer and Chandrasekharan \cite{Ayyar:2014eua}. We present theoretical arguments and numerical evidence which support the idea that the system develops a mass gap for sufficiently strong four fermi coupling.{\it without} producing a symmetry breaking fermion bilinear condensate. Massless and massive phases appear to be separated by a continuous phase transition.

Paper Structure

This paper contains 6 sections, 28 equations, 13 figures.

Table of Contents

  1. Introduction
  2. Lattice model and symmetries
  3. Auxiliary field representation
  4. Absence of bilinear condensates
  5. Phase structure
  6. Conclusions

Figures (13)

  • Figure 1: $<O_0>$ vs $G$ for $L=4,6,8,10$ and pbc
  • Figure 2: $<O_0>$ vs $m_0$ at $G=1.0$ for $L=6, 8,10$ and pbc
  • Figure 3: $<O_1>$ vs $G$ for $L=4,6,8,10$ and pbc
  • Figure 4: $<O_1>$ vs $m_1$ at $G=1.0$ for $L=6,8,10$ and pbc
  • Figure 5: $<O_2^1>$ and $<O_2^2>$ vs $G$ for $L=8$ and temporal apbc
  • ...and 8 more figures