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

Misumi, Tatsuhiro; Tanizaki, Yuya; Ünsal, Mithat

doi:10.1007/jhep07(2019)018

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 R² and its compactification to R× S¹_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 conditions satisfy volume independence.

Authors:

Misumi, Tatsuhiro ^[1]; Tanizaki, Yuya ^[2]; Ünsal, Mithat ^[2]

Akita Univ. (Japan); Inst. of Physical and Chemical Research (RIKEN), Wako (Japan); Keio Univ. (Japan)
North Carolina State Univ., Raleigh, NC (United States)

Publication Date:: Wed Jul 03 00:00:00 EDT 2019

Research Org.:: North Carolina State University, Raleigh, NC (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1609453

Grant/Contract Number:: FG02-03ER41260

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: 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.

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                    Misumi, Tatsuhiro, Tanizaki, Yuya, & Ünsal, Mithat. Fractional θ angle, ’t Hooft anomaly, and quantum instantons in charge-q multi-flavor Schwinger model.  United States.  https://doi.org/10.1007/jhep07(2019)018

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                    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.  https://doi.org/10.1007/jhep07(2019)018.  https://www.osti.gov/servlets/purl/1609453.

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@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)},

  number       = 7,

  volume       = 2019,

  place        = {United States},

  year         = {Wed Jul 03 00:00:00 EDT 2019},

  month        = {Wed Jul 03 00:00:00 EDT 2019}

}

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Kouno, Hiroaki; Makiyama, Takahiro; Sasaki, Takahiro
Journal of Physics G: Nuclear and Particle Physics, Vol. 40, Issue 9
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Differences and similarities between fundamental and adjoint matters in $S U (N)$ gauge theories
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Kouno, Hiroaki; Misumi, Tatsuhiro; Kashiwa, Kouji
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Kouno, Hiroaki; Kashiwa, Kouji; Takahashi, Junichi
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Path-integral representation for tunneling amplitudes in the Schwinger model
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Rothe, K. D.; Swieca, J. A.
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Generalization of the Haldane conjecture to SU(3) chains
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Lajkó, Miklós; Wamer, Kyle; Mila, Frédéric
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Fractons in the twisted multiflavor Schwinger model
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Shifman, M. A.; Smilga, A. V.
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Hetrick, J. E.; Hosotani, Y.; Iso, S.
Physical Review D, Vol. 53, Issue 12
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Bose-Fermi cancellations without supersymmetry
journal, May 2019

Cherman, Aleksey; Shifman, Mikhail; Ünsal, Mithat
Physical Review D, Vol. 99, Issue 10
DOI: 10.1103/physrevd.99.105001

Differences and similarities between fundamental and adjoint matters in SU(N) gauge theories
text, January 2013

Kouno, Hiroaki; Misumi, Tatsuhiro; Kashiwa, Kouji
arXiv
DOI: 10.48550/arxiv.1304.3274

C-P-T anomaly matching in bosonic quantum field theory and spin chains
text, January 2018

Sulejmanpasic, Tin; Tanizaki, Yuya
arXiv
DOI: 10.48550/arxiv.1802.02153

The Massive Multi-flavor Schwinger Model
text, January 1995

Hetrick, J. E.; Hosotani, Y.; Iso, S.
arXiv
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Works referencing / citing this record:

Self-conjugate QCD
journal, October 2019

Anber, Mohamed M.
Journal of High Energy Physics, Vol. 2019, Issue 10
DOI: 10.1007/jhep10(2019)042

Undoing decomposition
journal, December 2019

Sharpe, Eric
International Journal of Modern Physics A, Vol. 34, Issue 35
DOI: 10.1142/s0217751x19502336

Higher-form symmetries and 3-group in axion electrodynamics
journal, September 2020

Hidaka, Yoshimasa; Nitta, Muneto; Yokokura, Ryo
Physics Letters B, Vol. 808
DOI: 10.1016/j.physletb.2020.135672

Strongly coupled QFT dynamics via TQFT coupling
text, January 2020

Ünsal, Mithat
arXiv
DOI: 10.48550/arxiv.2007.03880

Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond $N$-ality
text, January 2021

Nguyen, Mendel; Tanizaki, Yuya; Ünsal, Mithat
arXiv
DOI: 10.48550/arxiv.2101.02227

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

Abstract

Citation Formats

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

Theta, time reversal and temperature journal, May 2017

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

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

Generalized global symmetries journal, February 2015

Quantum electrodynamics in two dimensions journal, November 1971

Time reversal, S U ( N ) Yang–Mills and cobordisms: Interacting topological superconductors/insulators and quantum spin liquids in 3 + 1 D journal, July 2018

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

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

Critical theory of quantum spin chains journal, October 1987

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

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

Naturalness, Chiral Symmetry, and Spontaneous Chiral Symmetry Breaking book, January 1980

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

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

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

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

Circle compactification and ’t Hooft anomaly journal, December 2017

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

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

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

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

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

Path integral for gauge theories with fermions journal, May 1980

On time-reversal anomaly of 2+1d topological phases journal, March 2017

Anomaly matching for the phase diagram of massless Z N -QCD journal, March 2018

Relating ’t Hooft anomalies of 4d pure Yang-Mills and 2d ℂℙN− 1 model journal, October 2018

Anomaly and global inconsistency matching: θ angles, S U ( 3 ) / U ( 1 ) 2 nonlinear sigma model, S U ( 3 ) chains, and generalizations journal, September 2018

Phase structure of the twisted SU(3)/U(1)2 flag sigma model on ℝ × S1 journal, February 2019

Chiral symmetry breaking without bilinear condensates, unbroken axial Z N symmetry, and exact QCD inequalities journal, November 1998

Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State journal, April 1983

Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model journal, February 1983

Resurgence and trans-series in Quantum Field Theory: the $\mathbb{C}{{\mathbb{P}}^{N-1 }}$ model journal, November 2012

QCD-like theories on R 3 × S 1 : A smooth journey from small to large r ( S 1 ) with double-trace deformations journal, September 2008

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

Theta, time reversal and temperature
journal, May 2017

$C − P − T$ 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

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

Generalized global symmetries
journal, February 2015

Quantum electrodynamics in two dimensions
journal, November 1971

Time reversal, $S U (N)$ Yang–Mills and cobordisms: Interacting topological superconductors/insulators and quantum spin liquids in $3 + 1 D$
journal, July 2018

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

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

Critical theory of quantum spin chains
journal, October 1987

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

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

Naturalness, Chiral Symmetry, and Spontaneous Chiral Symmetry Breaking
book, January 1980

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

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

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

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

Circle compactification and ’t Hooft anomaly
journal, December 2017

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

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

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

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

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

Path integral for gauge theories with fermions
journal, May 1980

On time-reversal anomaly of 2+1d topological phases
journal, March 2017

Anomaly matching for the phase diagram of massless $Z_{N}$ -QCD
journal, March 2018

Relating ’t Hooft anomalies of 4d pure Yang-Mills and 2d ℂℙN− 1 model
journal, October 2018

Anomaly and global inconsistency matching: $θ$ angles, $S U (3) / U {(1)}^{2}$ nonlinear sigma model, $S U (3)$ chains, and generalizations
journal, September 2018

Phase structure of the twisted SU(3)/U(1)2 flag sigma model on ℝ × S1
journal, February 2019

Chiral symmetry breaking without bilinear condensates, unbroken axial $Z_{N}$ symmetry, and exact QCD inequalities
journal, November 1998

Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State
journal, April 1983

Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model
journal, February 1983

Resurgence and trans-series in Quantum Field Theory: the $\mathbb{C}{{\mathbb{P}}^{N-1 }}$ model
journal, November 2012

QCD-like theories on $R_{3} \times S_{1}$ : A smooth journey from small to large $r (S_{1})$ with double-trace deformations
journal, September 2008

Continuity and Resurgence: Towards a continuum definition of the $C P (N - 1)$ model
journal, January 2013

Deconfinement in $ \mathcal{N}=1 $ super Yang-Mills theory on $ {{\mathbb{R}}^3}\times {{\mathbb{S}}^1} $ via dual-Coulomb gas and “affine” XY-model
journal, November 2013

Adjoint QCD on ℝ3 × S 1 with twisted fermionic boundary conditions
journal, June 2014