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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:
;
Publication Date:
Research Org.:
Syracuse Univ., NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
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

Citation Formats

Catterall, Simon, and Butt, Nouman. Topology and strong four fermion interactions in four dimensions. United States: N. p., 2018. Web. doi:10.1103/PhysRevD.97.094502.
Catterall, Simon, & Butt, Nouman. Topology and strong four fermion interactions in four dimensions. United States. doi:10.1103/PhysRevD.97.094502.
Catterall, Simon, and Butt, Nouman. Mon . "Topology and strong four fermion interactions in four dimensions". United States. doi:10.1103/PhysRevD.97.094502.
@article{osti_1436213,
title = {Topology and strong four fermion interactions in four dimensions},
author = {Catterall, Simon and Butt, Nouman},
abstractNote = {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.},
doi = {10.1103/PhysRevD.97.094502},
journal = {Physical Review D},
number = 9,
volume = 97,
place = {United States},
year = {2018},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.97.094502

Citation Metrics:
Cited by: 2 works
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