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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:
 [1];  [1];  [1]
  1. 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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Works referenced in this record:

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

  • Kähler, Erich
  • Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, Vol. 25, Issue 3-4
  • DOI: 10.1007/BF02992927

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

  • Becher, P.; Joos, H.
  • Zeitschrift für Physik C Particles and Fields, Vol. 15, Issue 4
  • DOI: 10.1007/BF01614426

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