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Title: Phase ambiguity of the measure for continuum Majorana fermions

Abstract

Integrating over a continuum Majorana fermion formally yields a functional pfaffian. We show that the phase of this pfaffian is ambiguous, as it depends on the choice of basis. This ambiguity is naturally resolved within a non-perturbative lattice definition, allowing us to discuss the relation between the phase of the lattice pfaffian and the effective θ angle of the theory. We also resolve an apparent paradox regarding the induced θ angle when a theory of N Dirac fermions in a real representation of the gauge group is re-expressed in terms of 2N Majorana fermions. We discuss how all this is reflected in chiral perturbation theory.

Authors:
;
Publication Date:
Research Org.:
San Francisco State Univ., CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); Israel Science Foundation (ISF)
OSTI Identifier:
1550589
Alternate Identifier(s):
OSTI ID: 1594606
Report Number(s):
arXiv:1904.08600v3
Journal ID: ISSN 2470-0010; PRVDAQ; 034507
Grant/Contract Number:  
FG03-92ER40711; SC0013682; 491/17
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 3; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Effective field theory; Lattice field theory; Path integrals

Citation Formats

Golterman, Maarten, and Shamir, Yigal. Phase ambiguity of the measure for continuum Majorana fermions. United States: N. p., 2019. Web. doi:10.1103/PhysRevD.100.034507.
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Golterman, Maarten, & Shamir, Yigal. Phase ambiguity of the measure for continuum Majorana fermions. United States. doi:10.1103/PhysRevD.100.034507.
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Golterman, Maarten, and Shamir, Yigal. Fri . "Phase ambiguity of the measure for continuum Majorana fermions". United States. doi:10.1103/PhysRevD.100.034507.
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@article{osti_1550589,
title = {Phase ambiguity of the measure for continuum Majorana fermions},
author = {Golterman, Maarten and Shamir, Yigal},
abstractNote = {Integrating over a continuum Majorana fermion formally yields a functional pfaffian. We show that the phase of this pfaffian is ambiguous, as it depends on the choice of basis. This ambiguity is naturally resolved within a non-perturbative lattice definition, allowing us to discuss the relation between the phase of the lattice pfaffian and the effective θ angle of the theory. We also resolve an apparent paradox regarding the induced θ angle when a theory of N Dirac fermions in a real representation of the gauge group is re-expressed in terms of 2N Majorana fermions. We discuss how all this is reflected in chiral perturbation theory.},
doi = {10.1103/PhysRevD.100.034507},
journal = {Physical Review D},
number = 3,
volume = 100,
place = {United States},
year = {2019},
month = {8}
}
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DOI: 10.1103/PhysRevD.100.034507
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Works referenced in this record:

A method for simulating chiral fermions on the lattice
journal, August 1992

QCD at θ ∼ π
journal, May 1999

Lattice fermions: Species doubling, chiral invariance and the triangle anomaly
journal, May 1981

Dynamical symmetry breaking in two flavor SU(N) and SO(N) lattice gauge theories
journal, November 1983

Chiral symmetry on the lattice with Wilson fermions
journal, December 1985

Phase diagram of nondegenerate twisted mass fermions
journal, November 2014

Effective theory for quenched lattice QCD and the Aoki phase
journal, May 2005

  • Golterman, Maarten; Sharpe, Stephen R.; Singleton, Robert L.
  • Physical Review D, Vol. 71, Issue 9
  • DOI: 10.1103/PhysRevD.71.094503

Susskind fermions on a euclidean lattice
journal, November 1981

Axial symmetries in lattice QCD with Kaplan fermions
journal, April 1995

Erratum: Lattice fermions and θ vacuums
journal, July 1982

Phase structure with nonzero Θ QCD and twisted mass fermions
journal, November 2015

Effective potential in ultraviolet completions for composite Higgs models
journal, May 2018

Spectrum of Dirac operator and role of winding number in QCD
journal, December 1992

Spectroscopy of SU(4) gauge theory with two flavors of sextet fermions
journal, June 2015

Large N chiral dynamics
journal, September 1980

Chiral dynamics in the large N limit
journal, January 1980

Technicolor and other QCD-like theories at next-to-next-to-leading order
journal, November 2009

New phase structure for lattice QCD with Wilson fermions
journal, December 1984

Chiral perturbation theory for the quenched approximation of QCD
journal, July 1992

Anomalies and chiral defect fermions
journal, April 1994

Lattice fermions and θ vacuums
journal, April 1982

One-loop chiral perturbation theory with two fermion representations
journal, July 2016

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