Topological fermion condensates from anomalies

Catterall, Simon; Laiho, Jack; Unmuth-Yockey, Judah

doi:10.1007/JHEP10(2018)013

Title: 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:

Catterall, Simon ^[1]; Laiho, Jack ^[1]; Unmuth-Yockey, Judah ^[1]

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

Publication Date:: Tue Oct 02 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:: 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.

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

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

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@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         = {Tue Oct 02 00:00:00 EDT 2018},

  month        = {Tue Oct 02 00:00:00 EDT 2018}

}

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https://doi.org/10.1007/JHEP10(2018)013

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Cited by: 14 works

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Works referenced in this record:

Symmetry Breaking through Bell-Jackiw Anomalies
journal, July 1976

't Hooft, G.
Physical Review Letters, Vol. 37, Issue 1
DOI: 10.1103/PhysRevLett.37.8

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Catterall, Simon; Kaplan, David B.; Ünsal, Mithat
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Kähler, Erich
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, Vol. 25, Issue 3-4
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Becher, P.; Joos, H.
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journal, September 2017

Laiho, J.; Bassler, S.; Coumbe, D.
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Simulations of dynamically triangulated gravity — an algorithm for arbitrary dimension
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Homology theory of lattice fermion doubling
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Rabin, Jeffrey M.
Nuclear Physics B, Vol. 201, Issue 2
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Title: Topological fermion condensates from anomalies

Abstract

Citation Formats

Symmetry Breaking through Bell-Jackiw Anomalies journal, July 1976

Geometric fermions journal, November 1982

Exact lattice supersymmetry journal, November 2009

Der innere Differentialkalkül journal, August 1962

The Dirac-Kähler equation and fermions on the lattice journal, December 1982

Lattice fermions journal, November 1977

Lattice quantum gravity and asymptotic safety journal, September 2017

Simulations of dynamically triangulated gravity — an algorithm for arbitrary dimension journal, June 1995

Homology theory of lattice fermion doubling journal, June 1982

Symmetry Breaking through Bell-Jackiw Anomalies
journal, July 1976

Geometric fermions
journal, November 1982

Exact lattice supersymmetry
journal, November 2009

Der innere Differentialkalkül
journal, August 1962

The Dirac-Kähler equation and fermions on the lattice
journal, December 1982

Lattice fermions
journal, November 1977

Lattice quantum gravity and asymptotic safety
journal, September 2017

Simulations of dynamically triangulated gravity — an algorithm for arbitrary dimension
journal, June 1995

Homology theory of lattice fermion doubling
journal, June 1982