# 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}

}

DOI: 10.1103/PhysRevD.97.094502

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Works referencing / citing this record:

##
Why is the mission impossible? Decoupling the mirror Ginsparg–Wilson fermions in the lattice models for two-dimensional Abelian chiral gauge theories

journal, July 2019

- Kikukawa, Y.
- Progress of Theoretical and Experimental Physics, Vol. 2019, Issue 7

##
Why is the mission impossible? Decoupling the mirror Ginsparg–Wilson fermions in the lattice models for two-dimensional Abelian chiral gauge theories

journal, July 2019

- Kikukawa, Y.
- Progress of Theoretical and Experimental Physics, Vol. 2019, Issue 7