Title: Topology and strong four fermion interactions in four dimensions

Abstract

We study massless fermions interacting through a particular four-fermion term in four dimensions. Exact symmetries prevent the generation of bilinear fermion mass terms. We determine the structure of the low-energy effective action for the auxiliary field needed to generate the four-fermion term and find it has an novel structure that admits topologically nontrivial defects with nonzero Hopf invariant. We show that fermions propagating in such a background pick up a mass without breaking symmetries. Furthermore, pairs of such defects experience a logarithmic interaction. We argue that a phase transition separates a phase where these defects proliferate from a broken phase where they are bound tightly. We conjecture that, by tuning one additional operator, the broken phase can be eliminated with a single BKT-like phase transition separating the massless from massive phases.

Authors:

Catterall, Simon; Butt, Nouman

Publication Date:

Mon May 07 00:00:00 EDT 2018

Research Org.:

Syracuse Univ., NY (United States)

Sponsoring Org.:

USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:

1436213

Alternate Identifier(s):

OSTI ID: 1498878

Grant/Contract Number:  

SC0009998

Resource Type:

Published Article

Journal Name:

Physical Review D

Additional Journal Information:

Journal Name: Physical Review D Journal Volume: 97 Journal Issue: 9; Journal ID: ISSN 2470-0010

Publisher:

American Physical Society

Country of Publication:

United States

Language:

English

Subject:

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; lattice field theory; nonperturbative effects in field theory; sigma models