skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Fractional θ angle, ’t Hooft anomaly, and quantum instantons in charge-q multi-flavor Schwinger model

Abstract

This work examines non-perturbative dynamics of a 2-dimensional QFT by using discrete ’t Hooft anomaly, semi-classics with circle compactification and bosonization. We focus on charge- q N-flavor Schwinger model, and also Wess-Zumino-Witten model. We first apply the recent developments of discrete ’t Hooft anomaly matching to theories on R 2 and its compactification to R× S 1 L. We then compare the ’t Hooft anomaly with dynamics of the models by explicitly constructing eigenstates and calculating physical quantities on the cylinder spacetime with periodic and flavor-twisted boundary conditions. We find different boundary conditions realize different anomalies. Especially under the twisted boundary conditions, there are Nq vacua associated with discrete chiral symmetry breaking. Chiral condensates for this case have fractional θ dependence e iθ/Nq, which provides the Nq-branch structure with soft fermion mass. We show that these behaviors at a small circumference cannot be explained by usual instantons but should be understood by “quantum” instantons, which saturate the BPS bound between classical action and quantum-induced effective potential. The effects of the quantum-instantons match the exact results obtained via bosonization within the region of applicability of semi-classics. We also argue that large- N limit of the Schwinger model with twisted boundary conditionsmore » satisfy volume independence.« less

Authors:
 [1];  [2];  [2]
  1. Akita Univ. (Japan); Inst. of Physical and Chemical Research (RIKEN), Wako (Japan); Keio Univ. (Japan)
  2. North Carolina State Univ., Raleigh, NC (United States)
Publication Date:
Research Org.:
North Carolina State Univ., Raleigh, NC (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1609453
Grant/Contract Number:  
FG02-03ER41260
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Volume: 2019; Journal Issue: 7; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Physics

Citation Formats

Misumi, Tatsuhiro, Tanizaki, Yuya, and Ünsal, Mithat. Fractional θ angle, ’t Hooft anomaly, and quantum instantons in charge-q multi-flavor Schwinger model. United States: N. p., 2019. Web. doi:10.1007/jhep07(2019)018.
Misumi, Tatsuhiro, Tanizaki, Yuya, & Ünsal, Mithat. Fractional θ angle, ’t Hooft anomaly, and quantum instantons in charge-q multi-flavor Schwinger model. United States. doi:10.1007/jhep07(2019)018.
Misumi, Tatsuhiro, Tanizaki, Yuya, and Ünsal, Mithat. Wed . "Fractional θ angle, ’t Hooft anomaly, and quantum instantons in charge-q multi-flavor Schwinger model". United States. doi:10.1007/jhep07(2019)018. https://www.osti.gov/servlets/purl/1609453.
@article{osti_1609453,
title = {Fractional θ angle, ’t Hooft anomaly, and quantum instantons in charge-q multi-flavor Schwinger model},
author = {Misumi, Tatsuhiro and Tanizaki, Yuya and Ünsal, Mithat},
abstractNote = {This work examines non-perturbative dynamics of a 2-dimensional QFT by using discrete ’t Hooft anomaly, semi-classics with circle compactification and bosonization. We focus on charge-q N-flavor Schwinger model, and also Wess-Zumino-Witten model. We first apply the recent developments of discrete ’t Hooft anomaly matching to theories on R2 and its compactification to R× S1L. We then compare the ’t Hooft anomaly with dynamics of the models by explicitly constructing eigenstates and calculating physical quantities on the cylinder spacetime with periodic and flavor-twisted boundary conditions. We find different boundary conditions realize different anomalies. Especially under the twisted boundary conditions, there are Nq vacua associated with discrete chiral symmetry breaking. Chiral condensates for this case have fractional θ dependence eiθ/Nq, which provides the Nq-branch structure with soft fermion mass. We show that these behaviors at a small circumference cannot be explained by usual instantons but should be understood by “quantum” instantons, which saturate the BPS bound between classical action and quantum-induced effective potential. The effects of the quantum-instantons match the exact results obtained via bosonization within the region of applicability of semi-classics. We also argue that large-N limit of the Schwinger model with twisted boundary conditions satisfy volume independence.},
doi = {10.1007/jhep07(2019)018},
journal = {Journal of High Energy Physics (Online)},
issn = {1029-8479},
number = 7,
volume = 2019,
place = {United States},
year = {2019},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models
journal, November 1966


Anomaly matching in QCD thermal phase transition
journal, May 2019


Vacuum structure of bifundamental gauge theories at finite topological angles
journal, June 2017


Abelian Duality, Confinement, and Chiral-Symmetry Breaking in a SU(2) QCD-Like Theory
journal, January 2008


Anomaly matching, (axial) Schwinger models, and high-T super Yang-Mills domain walls
journal, September 2018

  • Anber, Mohamed M.; Poppitz, Erich
  • Journal of High Energy Physics, Vol. 2018, Issue 9
  • DOI: 10.1007/JHEP09(2018)076

Theta, time reversal and temperature
journal, May 2017

  • Gaiotto, Davide; Kapustin, Anton; Komargodski, Zohar
  • Journal of High Energy Physics, Vol. 2017, Issue 5
  • DOI: 10.1007/JHEP05(2017)091

Chiral Lagrangian from Duality and Monopole Operators in Compactified QCD
journal, August 2016


C P T anomaly matching in bosonic quantum field theory and spin chains
journal, April 2018


Anomalies and fermion zero modes on strings and domain walls
journal, January 1985


The “parity” anomaly on an unorientable manifold
journal, November 2016


Constraints on supersymmetry breaking
journal, July 1982


Generalization of the Haldane conjecture to SU(3) chains
journal, November 2017


Quantum distillation of Hilbert spaces, semi-classics and anomaly matching
journal, August 2018

  • Dunne, Gerald V.; Tanizaki, Yuya; Ünsal, Mithat
  • Journal of High Energy Physics, Vol. 2018, Issue 8
  • DOI: 10.1007/JHEP08(2018)068

Double-θ vacuum structure and the functional integral in the Schwinger model
journal, November 1980


Generalized global symmetries
journal, February 2015

  • Gaiotto, Davide; Kapustin, Anton; Seiberg, Nathan
  • Journal of High Energy Physics, Vol. 2015, Issue 2
  • DOI: 10.1007/JHEP02(2015)172

Quantum electrodynamics in two dimensions
journal, November 1971


Reduction of Dynamical Degrees of Freedom in the Large- N Gauge Theory
journal, April 1982


High-temperature domain walls of QCD with imaginary chemical potentials
journal, June 2019

  • Nishimura, Hiromichi; Tanizaki, Yuya
  • Journal of High Energy Physics, Vol. 2019, Issue 6
  • DOI: 10.1007/JHEP06(2019)040

Semiclassical Realization of Infrared Renormalons
journal, September 2012


Hamiltonian Formulation of the Schwinger Model: Non-Confinement and Screening of the Charge
journal, July 1990


Time-reversal breaking in QCD4, walls, and dualities in 2 + 1 dimensions
journal, January 2018

  • Gaiotto, Davide; Komargodski, Zohar; Seiberg, Nathan
  • Journal of High Energy Physics, Vol. 2018, Issue 1
  • DOI: 10.1007/JHEP01(2018)110

Domain walls in high-T SU(N) super Yang-Mills theory and QCD(adj)
journal, May 2019

  • Anber, Mohamed M.; Poppitz, Erich
  • Journal of High Energy Physics, Vol. 2019, Issue 5
  • DOI: 10.1007/JHEP05(2019)151

Critical theory of quantum spin chains
journal, October 1987


Lattice study on QCD-like theory with exact center symmetry
journal, November 2015

  • Iritani, Takumi; Itou, Etsuko; Misumi, Tatsuhiro
  • Journal of High Energy Physics, Vol. 2015, Issue 11
  • DOI: 10.1007/JHEP11(2015)159

The Schwinger model and its axial anomaly
journal, January 1985


Gauge Invariance and Mass. II
journal, December 1962


Haldane limits via Lagrangian embeddings
journal, February 2012


A PCAC puzzle: π0→γγ in the σ-model
journal, March 1969


Theory of nonabelian goldstone bosons in two dimensions
journal, November 1983


Goldstone fields in two dimensions with multivalued actions
journal, June 1984


The quenched Eguchi-Kawai model
journal, June 1982


Coupling a QFT to a TQFT and duality
journal, April 2014


Path-Integral Measure for Gauge-Invariant Fermion Theories
journal, April 1979


Global aspects of current algebra
journal, August 1983


Confinement in the Bulk, Deconfinement on the Wall: Infrared Equivalence between Compactified QCD and Quantum Magnets
journal, September 2017


Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking
journal, August 2018


Consequences of anomalous ward identities
journal, November 1971


Vacuum structure of charge k two-dimensional QED and dynamics of an anti D-string near an O1−-plane
journal, March 2019


Continuity, deconfinement, and (super) Yang-Mills theory
journal, October 2012

  • Poppitz, Erich; Schäfer, Thomas; Ünsal, Mithat
  • Journal of High Energy Physics, Vol. 2012, Issue 10
  • DOI: 10.1007/JHEP10(2012)115

Comments on abelian Higgs models and persistent order
journal, January 2019


More about the massive Schwinger model
journal, September 1976


Volume independence in large N c QCD-like gauge theories
journal, June 2007


New Nonperturbative Methods in Quantum Field Theory: From Large- N Orbifold Equivalence to Bions and Resurgence
journal, October 2016


Gauge Invariance and Mass
journal, January 1962


Volume Independence in the Large N Limit and an Emergent Fermionic Symmetry
journal, September 2013


Multi-flavor massless QED2 at finite densities via Lefschetz thimbles
journal, February 2017


Axial-Vector Vertex in Spinor Electrodynamics
journal, January 1969


Field-Theory Representation of Gauge-Gravity Symmetry-Protected Topological Invariants, Group Cohomology, and Beyond
journal, January 2015


On the realization of chiral symmetry in (1+1) dimensions
journal, March 1986


Global Symmetries, Volume Independence, and Continuity in Quantum Field Theories
journal, January 2017


The curious incident of multi-instantons and the necessity of Lefschetz thimbles
journal, November 2015

  • Behtash, Alireza; Poppitz, Erich; Sulejmanpasic, Tin
  • Journal of High Energy Physics, Vol. 2015, Issue 11
  • DOI: 10.1007/JHEP11(2015)175

The axial anomaly and the bound-state spectrum in confining theories
journal, January 1981


Circle compactification and ’t Hooft anomaly
journal, December 2017

  • Tanizaki, Yuya; Misumi, Tatsuhiro; Sakai, Norisuke
  • Journal of High Energy Physics, Vol. 2017, Issue 12
  • DOI: 10.1007/JHEP12(2017)056

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
journal, August 2012

  • Argyres, Philip C.; Ünsal, Mithat
  • Journal of High Energy Physics, Vol. 2012, Issue 8
  • DOI: 10.1007/JHEP08(2012)063

The massive multi-flavor Schwinger model
journal, May 1995


Topological fluctuations and breaking of chiral symmetry in gauge theories involving massless fermions
journal, March 1977


Path-integral representation for tunneling amplitudes in the Schwinger model
journal, February 1979


Charge shielding and quark confinement in the massive schwinger model
journal, September 1975


Walls, anomalies, and deconfinement in quantum antiferromagnets
journal, February 2018


Sigma models on flags
journal, January 2019


A proof of part of Haldane's conjecture on spin chains
journal, July 1986

  • Affleck, Ian; Lieb, Elliott H.
  • Letters in Mathematical Physics, Vol. 12, Issue 1
  • DOI: 10.1007/BF00400304

Finite size phase transitions in QCD with adjoint fermions
journal, July 2009


Chiral symmetry breaking with no bilinear condensate revisited
journal, October 2015


Non-abelian bosonization in two dimensions
journal, December 1984

  • Witten, Edward
  • Communications in Mathematical Physics, Vol. 92, Issue 4
  • DOI: 10.1007/BF01215276

Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions
journal, August 2018


Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles
journal, October 2015

  • Cherman, Aleksey; Dorigoni, Daniele; Ünsal, Mithat
  • Journal of High Energy Physics, Vol. 2015, Issue 10
  • DOI: 10.1007/JHEP10(2015)056

There are no Goldstone bosons in two dimensions
journal, December 1973

  • Coleman, Sidney
  • Communications in Mathematical Physics, Vol. 31, Issue 4
  • DOI: 10.1007/BF01646487