Duality web on a 3D Euclidean lattice and manifestation of hidden symmetries

Son, Jun Ho; Chen, Jing -Yuan; Raghu, S.

doi:10.1007/jhep06(2019)038

Title: Duality web on a 3D Euclidean lattice and manifestation of hidden symmetries

Abstract

We generalize our previous lattice construction of the abelian bosonization duality in 2 + 1 dimensions to the entire web of dualities as well as the N_f = 2 self-duality, via the lattice implementation of a set of modular transformations in the theory space. The microscopic construction provides explicit operator mappings, and allows the manifestation of some hidden symmetries. It also exposes certain caveats and implicit assumptions beneath the usual application of the modular transformations to generate the web of dualities. Lastly, we make brief comments on the non-relativistic limit of the dualities.

Authors:

Son, Jun Ho ^[1]; Chen, Jing -Yuan ^[1]; Raghu, S. ^[2]

Stanford Univ., Stanford, CA (United States)
Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)

Publication Date:: Tue Jun 11 00:00:00 EDT 2019

Research Org.:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1532404

Grant/Contract Number:: AC02-76SF00515

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: 6; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Duality in Gauge Field Theories; Lattice Quantum Field Theory; Nonperturbative Effects

Citation Formats


                    Son, Jun Ho, Chen, Jing -Yuan, and Raghu, S. Duality web on a 3D Euclidean lattice and manifestation of hidden symmetries.  United States: N. p., 2019. 
Web.  doi:10.1007/jhep06(2019)038.

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                    Son, Jun Ho, Chen, Jing -Yuan, & Raghu, S. Duality web on a 3D Euclidean lattice and manifestation of hidden symmetries.  United States.  https://doi.org/10.1007/jhep06(2019)038

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                    Son, Jun Ho, Chen, Jing -Yuan, and Raghu, S. Tue .  
"Duality web on a 3D Euclidean lattice and manifestation of hidden symmetries".  United States.  https://doi.org/10.1007/jhep06(2019)038.  https://www.osti.gov/servlets/purl/1532404.

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@article{osti_1532404,

  title        = {Duality web on a 3D Euclidean lattice and manifestation of hidden symmetries},

  author       = {Son, Jun Ho and Chen, Jing -Yuan and Raghu, S.},

  abstractNote = {We generalize our previous lattice construction of the abelian bosonization duality in 2 + 1 dimensions to the entire web of dualities as well as the Nf = 2 self-duality, via the lattice implementation of a set of modular transformations in the theory space. The microscopic construction provides explicit operator mappings, and allows the manifestation of some hidden symmetries. It also exposes certain caveats and implicit assumptions beneath the usual application of the modular transformations to generate the web of dualities. Lastly, we make brief comments on the non-relativistic limit of the dualities.},

  doi          = {10.1007/jhep06(2019)038},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 6,

  volume       = 2019,

  place        = {United States},

  year         = {Tue Jun 11 00:00:00 EDT 2019},

  month        = {Tue Jun 11 00:00:00 EDT 2019}

}

Copy to clipboard

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Works referencing / citing this record:

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Journal of High Energy Physics, Vol. 2019, Issue 10
DOI: 10.1007/jhep10(2019)288

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SciPost Physics, Vol. 7, Issue 1
DOI: 10.21468/scipostphys.7.1.007

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journal, February 2020

Aitken, Kyle; Baumgartner, Andrew; Choi, Changha
Journal of High Energy Physics, Vol. 2020, Issue 2
DOI: 10.1007/jhep02(2020)060

Phases of Flavor Broken QCD$_3$
text, January 2019

Baumgartner, Andrew
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DOI: 10.48550/arxiv.1905.04267

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Title: Duality web on a 3D Euclidean lattice and manifestation of hidden symmetries

Abstract

Citation Formats

Bosonization as duality journal, June 1994

Explicit Derivation of Duality between a Free Dirac Cone and Quantum Electrodynamics in ( 2 + 1 ) Dimensions journal, June 2016

Self-dual quantum electrodynamics as boundary state of the three-dimensional bosonic topological insulator journal, December 2015

Baryons, monopoles and dualities in Chern-Simons-matter theories journal, February 2016

Continuous transition between fractional quantum Hall and superfluid states journal, June 2014

Large scale physics of the quantum hall fluid journal, October 1991

Boson localization and the superfluid-insulator transition journal, July 1989

Mirror symmetry in three dimensional gauge theories journal, October 1996

Exact Boson-Fermion Duality on a 3D Euclidean Lattice journal, January 2018

Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators journal, June 2016

Dual Dirac Liquid on the Surface of the Electron Topological Insulator journal, November 2015

A duality web in 2 + 1 dimensions and condensed matter physics journal, November 2016

Particle-Vortex Duality from 3D Bosonization text, January 2016

Effective-Field-Theory Model for the Fractional Quantum Hall Effect journal, January 1989

Mirror symmetry and the half-filled Landau level journal, December 2015

Non-Abelian fermionization and fractional quantum Hall transitions journal, February 2018

The fermion-boson mapping in three-dimensional quantum field theory journal, October 1994

Effective-Field-Theory Model for the Fractional Quantum Hall Effect journal, February 1989

Duality between ( 2 + 1 ) d quantum critical points journal, September 2019

Fermi-Bose Transmutations Induced by Gauge Fields journal, February 1988

Non-Abelian bosonization and modular transformation approach to superuniversality journal, March 2019

Phase Transition in a Lattice Model of Superconductivity journal, November 1981

Correspondence between two-dimensional bosons and a bulk superconductor in a magnetic field journal, February 1989

Fractional Statistics and the Quantum Hall Effect journal, August 1984

Particle-Vortex Duality from 3D Bosonization journal, September 2016

Composite-fermion approach for the fractional quantum Hall effect journal, July 1989

Global phase diagram in the quantum Hall effect journal, July 1992

Mandelstam-'t Hooft duality in abelian lattice models journal, July 1978

Fermi-Bose Transmutations Induced by Gauge Fields journal, February 1988

Physics of Three-Dimensional Bosonic Topological Insulators: Surface-Deconfined Criticality and Quantized Magnetoelectric Effect journal, February 2013

More Abelian dualities in 2 + 1 dimensions text, January 2017

Particle-vortex symmetric liquid journal, January 2017

On mirror symmetry in three dimensional Abelian gauge theories journal, April 1999

Mott transition in an anyon gas journal, November 1993

Topological orders and edge excitations in fractional quantum Hall states journal, October 1995

Modular invariance, self-duality and the phase transition between quantum Hall plateaus journal, September 1996

Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect text, January 2012

Is the Composite Fermion a Dirac Particle? text, January 2015

Mirror symmetry and the half-filled Landau level text, January 2015

Baryons, monopoles and dualities in Chern-Simons-matter theories text, January 2015

Particle-vortex symmetric liquid text, January 2016

Symmetry and duality in bosonization of two-dimensional Dirac fermions text, January 2017

Exact Boson-Fermion Duality on a 3D Euclidean Lattice text, January 2017

Non-Abelian Fermionization and Fractional Quantum Hall Transitions text, January 2017

$\mathcal{N}{=}1$ dualities in 2+1 dimensions text, January 2018

The Fermion-Boson Mapping in Three Dimensional Quantum Field Theory text, January 1994

Mirror Symmetry in Three Dimensional Gauge Theories text, January 1996

Bosonization and mirror symmetry journal, October 2016

Is the Composite Fermion a Dirac Particle? journal, September 2015

Symmetry and Duality in Bosonization of Two-Dimensional Dirac Fermions journal, October 2017

Mirror symmetry and the half-filled Landau level text, January 2015

Phases of flavor broken QCD3 journal, October 2019

A web of 2d dualities: ${\bf Z}_2$ gauge fields and Arf invariants journal, January 2019

Generalization of QCD3 symmetry-breaking and flavored quiver dualities journal, February 2020

Phases of Flavor Broken QCD$_3$ text, January 2019

Bosonization as duality
journal, June 1994

Explicit Derivation of Duality between a Free Dirac Cone and Quantum Electrodynamics in ( $2 + 1$ ) Dimensions
journal, June 2016

Self-dual quantum electrodynamics as boundary state of the three-dimensional bosonic topological insulator
journal, December 2015

Baryons, monopoles and dualities in Chern-Simons-matter theories
journal, February 2016

Continuous transition between fractional quantum Hall and superfluid states
journal, June 2014

Large scale physics of the quantum hall fluid
journal, October 1991

Boson localization and the superfluid-insulator transition
journal, July 1989

Mirror symmetry in three dimensional gauge theories
journal, October 1996

Exact Boson-Fermion Duality on a 3D Euclidean Lattice
journal, January 2018

Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators
journal, June 2016

Dual Dirac Liquid on the Surface of the Electron Topological Insulator
journal, November 2015

A duality web in $2 + 1$ dimensions and condensed matter physics
journal, November 2016

Particle-Vortex Duality from 3D Bosonization
text, January 2016

Effective-Field-Theory Model for the Fractional Quantum Hall Effect
journal, January 1989

Mirror symmetry and the half-filled Landau level
journal, December 2015

Non-Abelian fermionization and fractional quantum Hall transitions
journal, February 2018

The fermion-boson mapping in three-dimensional quantum field theory
journal, October 1994

Effective-Field-Theory Model for the Fractional Quantum Hall Effect
journal, February 1989

Duality between $(2 + 1) d$ quantum critical points
journal, September 2019

Fermi-Bose Transmutations Induced by Gauge Fields
journal, February 1988

Non-Abelian bosonization and modular transformation approach to superuniversality
journal, March 2019

Phase Transition in a Lattice Model of Superconductivity
journal, November 1981

Correspondence between two-dimensional bosons and a bulk superconductor in a magnetic field
journal, February 1989

Fractional Statistics and the Quantum Hall Effect
journal, August 1984

Particle-Vortex Duality from 3D Bosonization
journal, September 2016

Composite-fermion approach for the fractional quantum Hall effect
journal, July 1989

Global phase diagram in the quantum Hall effect
journal, July 1992

Mandelstam-'t Hooft duality in abelian lattice models
journal, July 1978

Fermi-Bose Transmutations Induced by Gauge Fields
journal, February 1988

Physics of Three-Dimensional Bosonic Topological Insulators: Surface-Deconfined Criticality and Quantized Magnetoelectric Effect
journal, February 2013

More Abelian dualities in 2 + 1 dimensions
text, January 2017

Particle-vortex symmetric liquid
journal, January 2017

On mirror symmetry in three dimensional Abelian gauge theories
journal, April 1999

Mott transition in an anyon gas
journal, November 1993

Topological orders and edge excitations in fractional quantum Hall states
journal, October 1995

Modular invariance, self-duality and the phase transition between quantum Hall plateaus
journal, September 1996

Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
text, January 2012

Is the Composite Fermion a Dirac Particle?
text, January 2015

Mirror symmetry and the half-filled Landau level
text, January 2015

Baryons, monopoles and dualities in Chern-Simons-matter theories
text, January 2015

Particle-vortex symmetric liquid
text, January 2016

Symmetry and duality in bosonization of two-dimensional Dirac fermions
text, January 2017

Exact Boson-Fermion Duality on a 3D Euclidean Lattice
text, January 2017

Non-Abelian Fermionization and Fractional Quantum Hall Transitions
text, January 2017

$\mathcal{N}{=}1$ dualities in 2+1 dimensions
text, January 2018

The Fermion-Boson Mapping in Three Dimensional Quantum Field Theory
text, January 1994

Mirror Symmetry in Three Dimensional Gauge Theories
text, January 1996

Bosonization and mirror symmetry
journal, October 2016

Is the Composite Fermion a Dirac Particle?
journal, September 2015

Symmetry and Duality in Bosonization of Two-Dimensional Dirac Fermions
journal, October 2017

Mirror symmetry and the half-filled Landau level
text, January 2015

Phases of flavor broken QCD3
journal, October 2019

A web of 2d dualities: ${\bf Z}_2$ gauge fields and Arf invariants
journal, January 2019

Generalization of QCD3 symmetry-breaking and flavored quiver dualities
journal, February 2020

Phases of Flavor Broken QCD$_3$
text, January 2019