# Topological fermion condensates from anomalies

## Abstract

We show that a class of fermion theory formulated on a compact, curved manifold will generate a condensate whose magnitude is determined only by the volume and Euler characteristic of the space. The construction requires that the fermions be treated as Kahler-Dirac fields and the condensate arises from an anomaly associated with a U(1) global symmetry which is subsequently broken to a discrete subgroup. Remarkably the anomaly survives under discretization of the space which allows us to compute the condensate on an arbitrary triangulation. The results, being topological in character, should hold in a wide range of gravitationally coupled fermion theories both classical and quantum.

- Authors:

- Syracuse Univ., NY (United States). Department of Physics

- Publication Date:

- Research Org.:
- Syracuse Univ., NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1483480

- Grant/Contract Number:
- [SC0009998]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- [Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 10]; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Lattice Models of Gravity; Lattice Quantum Field Theory; Nonperturbative Effects

### Citation Formats

```
Catterall, Simon, Laiho, Jack, and Unmuth-Yockey, Judah. Topological fermion condensates from anomalies. United States: N. p., 2018.
Web. doi:10.1007/JHEP10(2018)013.
```

```
Catterall, Simon, Laiho, Jack, & Unmuth-Yockey, Judah. Topological fermion condensates from anomalies. United States. doi:10.1007/JHEP10(2018)013.
```

```
Catterall, Simon, Laiho, Jack, and Unmuth-Yockey, Judah. Tue .
"Topological fermion condensates from anomalies". United States. doi:10.1007/JHEP10(2018)013. https://www.osti.gov/servlets/purl/1483480.
```

```
@article{osti_1483480,
```

title = {Topological fermion condensates from anomalies},

author = {Catterall, Simon and Laiho, Jack and Unmuth-Yockey, Judah},

abstractNote = {We show that a class of fermion theory formulated on a compact, curved manifold will generate a condensate whose magnitude is determined only by the volume and Euler characteristic of the space. The construction requires that the fermions be treated as Kahler-Dirac fields and the condensate arises from an anomaly associated with a U(1) global symmetry which is subsequently broken to a discrete subgroup. Remarkably the anomaly survives under discretization of the space which allows us to compute the condensate on an arbitrary triangulation. The results, being topological in character, should hold in a wide range of gravitationally coupled fermion theories both classical and quantum.},

doi = {10.1007/JHEP10(2018)013},

journal = {Journal of High Energy Physics (Online)},

number = [10],

volume = [2018],

place = {United States},

year = {2018},

month = {10}

}

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