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

Karch, Andreas; Tong, David; Turner, Carl

doi:10.21468/SciPostPhys.7.1.007

Title: A web of 2d dualities: $${\bf Z}_2$$ gauge fields and Arf invariants

Journal Article · Wed Jul 10 00:00:00 EDT 2019 · SciPost Physics

DOI:https://doi.org/10.21468/SciPostPhys.7.1.007· OSTI ID:1564290

Karch, Andreas ^[1]; Tong, David ^[2]; Turner, Carl ^[2]

University of Washington
University of Cambridge

We describe a web of well-known dualities connecting quantum field theories in d=1+1 dimensions. The web is constructed by gauging Z_2 $Z_{2}$ global symmetries and includes a number of perennial favourites such as the Jordan-Wigner transformation, Kramers-Wannier duality, bosonization of a Dirac fermion, and T-duality. There are also less-loved examples, such as non-modular invariant c=1 CFTs that depend on a background spin structure.

View Journal Article

Cite

Export

Save

Research Organization:: Univ. of Washington, Seattle, WA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0011637

OSTI ID:: 1564290

Alternate ID(s):: OSTI ID: 1595213

Journal Information:: SciPost Physics, Journal Name: SciPost Physics Vol. 7 Journal Issue: 1; ISSN 2542-4653

Publisher:: SciPost FoundationCopyright Statement

Country of Publication:: Netherlands

Language:: English

Citation Metrics:

Cited by: 51 works

Citation information provided by
Web of Science

References (53)

Is the Composite Fermion a Dirac Particle? Son, Dam Thanh Physical Review X, Vol. 5, Issue 3 https://doi.org/10.1103/PhysRevX.5.031027	journal	September 2015
Developments in topological gravity Dijkgraaf, Robbert; Witten, Edward International Journal of Modern Physics A, Vol. 33, Issue 30 https://doi.org/10.1142/S0217751X18300296	journal	October 2018
Bosonization and mirror symmetry Kachru, Shamit; Mulligan, Michael; Torroba, Gonzalo Physical Review D, Vol. 94, Issue 8 https://doi.org/10.1103/PhysRevD.94.085009	journal	October 2016
Fermionic SPT phases in higher dimensions and bosonization Kapustin, Anton; Thorngren, Ryan Journal of High Energy Physics, Vol. 2017, Issue 10 https://doi.org/10.1007/JHEP10(2017)080	journal	October 2017
Aspects of N = 2 supersymmetric gauge theories in three dimensions Aharony, O.; Hanany, A.; Intriligator, K. Nuclear Physics B, Vol. 499, Issue 1-2 https://doi.org/10.1016/S0550-3213(97)00323-4	journal	August 1997
Baryons, monopoles and dualities in Chern-Simons-matter theories Aharony, Ofer Journal of High Energy Physics, Vol. 2016, Issue 2 https://doi.org/10.1007/JHEP02(2016)093	journal	February 2016
Aspects of bosonization in string theory Elitzur, S.; Gross, E.; Rabinovici, E. Nuclear Physics B, Vol. 283 https://doi.org/10.1016/0550-3213(87)90281-1	journal	January 1987
Continuous transition between fractional quantum Hall and superfluid states Barkeshli, Maissam; McGreevy, John Physical Review B, Vol. 89, Issue 23 https://doi.org/10.1103/PhysRevB.89.235116	journal	June 2014
Exact Boson-Fermion Duality on a 3D Euclidean Lattice Chen, Jing-Yuan; Son, Jun Ho; Wang, Chao Physical Review Letters, Vol. 120, Issue 1 https://doi.org/10.1103/PhysRevLett.120.016602	journal	January 2018
Dual Dirac Liquid on the Surface of the Electron Topological Insulator Wang, Chong; Senthil, T. Physical Review X, Vol. 5, Issue 4 https://doi.org/10.1103/PhysRevX.5.041031	journal	November 2015
Anyon superconductivity and the fractional quantum Hall effect Lee, Dung-Hai; Fisher, Matthew P. A. Physical Review Letters, Vol. 63, Issue 8 https://doi.org/10.1103/PhysRevLett.63.903	journal	August 1989
Duality and bosonization of $(2 + 1)$ -dimensional Majorana fermions Metlitski, Max A.; Vishwanath, Ashvin; Xu, Cenke Physical Review B, Vol. 95, Issue 20 https://doi.org/10.1103/PhysRevB.95.205137	journal	May 2017
Emergent photons and transitions in the $O (3)$ sigma model with hedgehog suppression Motrunich, Olexei I.; Vishwanath, Ashvin Physical Review B, Vol. 70, Issue 7 https://doi.org/10.1103/PhysRevB.70.075104	journal	August 2004
Unpaired Majorana fermions in quantum wires Kitaev, A. Yu Physics-Uspekhi, Vol. 44, Issue 10S https://doi.org/10.1070/1063-7869/44/10S/S29	journal	October 2001
A master bosonization duality Jensen, Kristan Journal of High Energy Physics, Vol. 2018, Issue 1 https://doi.org/10.1007/JHEP01(2018)031	journal	January 2018
Quantum sine-Gordon equation as the massive Thirring model Coleman, Sidney Physical Review D, Vol. 11, Issue 8 https://doi.org/10.1103/PhysRevD.11.2088	journal	April 1975
Many-body topological invariants in fermionic symmetry-protected topological phases: Cases of point group symmetries Shiozaki, Ken; Shapourian, Hassan; Ryu, Shinsei Physical Review B, Vol. 95, Issue 20 https://doi.org/10.1103/PhysRevB.95.205139	journal	May 2017
Time-reversal symmetry, anomalies, and dualities in (2+1)$d$ Cordova, Clay; Hsin, Po-Shen; Seiberg, Nathan SciPost Physics, Vol. 5, Issue 1 https://doi.org/10.21468/SciPostPhys.5.1.006	journal	January 2018
Spin Structures and Quadratic forms on Surfaces Johnson, Dennis Journal of the London Mathematical Society, Vol. s2-22, Issue 2 https://doi.org/10.1112/jlms/s2-22.2.365	journal	October 1980
Two soluble models of an antiferromagnetic chain Lieb, Elliott; Schultz, Theodore; Mattis, Daniel Annals of Physics, Vol. 16, Issue 3 https://doi.org/10.1016/0003-4916(61)90115-4	journal	December 1961
Chern–Simons theory with vector fermion matter Giombi, Simone; Minwalla, Shiraz; Prakash, Shiroman The European Physical Journal C, Vol. 72, Issue 8 https://doi.org/10.1140/epjc/s10052-012-2112-0	journal	August 2012
Fermionic symmetry protected topological phases and cobordisms Kapustin, Anton; Thorngren, Ryan; Turzillo, Alex Journal of High Energy Physics, Vol. 2015, Issue 12 https://doi.org/10.1007/JHEP12(2015)052	journal	December 2015
Statistics of the Two-Dimensional Ferromagnet. Part I Kramers, H. A.; Wannier, G. H. Physical Review, Vol. 60, Issue 3 https://doi.org/10.1103/PhysRev.60.252	journal	August 1941
Mirror symmetry and toric geometry in three-dimensional gauge theories Dorey, Nick; Tong, David Journal of High Energy Physics, Vol. 2000, Issue 05 https://doi.org/10.1088/1126-6708/2000/05/018	journal	May 2000
Bosonization on higher genus Riemann surfaces Alvarez-Gaumé, Luis; Bost, Jean-Benoît; Moore, Gregory Communications in Mathematical Physics, Vol. 112, Issue 3 https://doi.org/10.1007/BF01218489	journal	September 1987
Fermi-Bose Transmutations Induced by Gauge Fields Polyakov, A. M. Modern Physics Letters A, Vol. 03, Issue 03 https://doi.org/10.1142/S0217732388000398	journal	February 1988
�ber das Paulische �quivalenzverbot Jordan, P.; Wigner, E. Zeitschrift f�r Physik, Vol. 47, Issue 9-10 https://doi.org/10.1007/BF01331938	journal	September 1928
Correlation functions of large N Chern-Simons-Matter theories and bosonization in three dimensions Aharony, Ofer; Gur-Ari, Guy; Yacoby, Ran Journal of High Energy Physics, Vol. 2012, Issue 12 https://doi.org/10.1007/JHEP12(2012)028	journal	December 2012
Explicit Derivation of Duality between a Free Dirac Cone and Quantum Electrodynamics in ( $2 + 1$ ) Dimensions Mross, David F.; Alicea, Jason; Motrunich, Olexei I. Physical Review Letters, Vol. 117, Issue 1 https://doi.org/10.1103/PhysRevLett.117.016802	journal	June 2016
Two-Dimensional Ising Model as a Soluble Problem of Many Fermions Schultz, T. D.; Mattis, D. C.; Lieb, E. H. Reviews of Modern Physics, Vol. 36, Issue 3 https://doi.org/10.1103/RevModPhys.36.856	journal	July 1964
Self-dual quantum electrodynamics as boundary state of the three-dimensional bosonic topological insulator Xu, Cenke; You, Yi-Zhuang Physical Review B, Vol. 92, Issue 22 https://doi.org/10.1103/PhysRevB.92.220416	journal	December 2015
Mott transition in an anyon gas Chen, Wei; Fisher, Matthew P. A.; Wu, Yong-Shi Physical Review B, Vol. 48, Issue 18 https://doi.org/10.1103/PhysRevB.48.13749	journal	November 1993
Comments on abelian Higgs models and persistent order Komargodski, Zohar; Sharon, Adar; Thorngren, Ryan SciPost Physics, Vol. 6, Issue 1 https://doi.org/10.21468/SciPostPhys.6.1.003	journal	January 2019
Deconfined Quantum Critical Points: Symmetries and Dualities Wang, Chong; Nahum, Adam; Metlitski, Max A. Physical Review X, Vol. 7, Issue 3 https://doi.org/10.1103/PhysRevX.7.031051	journal	September 2017
More Abelian dualities in 2 + 1 dimensions Karch, Andreas; Robinson, Brandon; Tong, David Journal of High Energy Physics, Vol. 2017, Issue 1 https://doi.org/10.1007/JHEP01(2017)017	journal	January 2017
Riemann surfaces and spin structures Atiyah, Michael F. Annales scientifiques de l'École normale supérieure, Vol. 4, Issue 1 https://doi.org/10.24033/asens.1205	journal	January 1971
Mirror symmetry in three dimensional gauge theories Intriligator, K.; Seiberg, N. Physics Letters B, Vol. 387, Issue 3 https://doi.org/10.1016/0370-2693(96)01088-X	journal	October 1996
Comments on global symmetries, anomalies, and duality in (2 + 1)d Benini, Francesco; Hsin, Po-Shen; Seiberg, Nathan Journal of High Energy Physics, Vol. 2017, Issue 4 https://doi.org/10.1007/JHEP04(2017)135	journal	April 2017
Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators Metlitski, Max A.; Vishwanath, Ashvin Physical Review B, Vol. 93, Issue 24 https://doi.org/10.1103/PhysRevB.93.245151	journal	June 2016
d = 3 bosonic vector models coupled to Chern-Simons gauge theories Aharony, Ofer; Gur-Ari, Guy; Yacoby, Ran Journal of High Energy Physics, Vol. 2012, Issue 3 https://doi.org/10.1007/JHEP03(2012)037	journal	March 2012
A duality web in $2 + 1$ dimensions and condensed matter physics Seiberg, Nathan; Senthil, T.; Wang, Chong Annals of Physics, Vol. 374 https://doi.org/10.1016/j.aop.2016.08.007	journal	November 2016
Mirror symmetry and bosonization in 2d and 3d Karch, Andreas; Tong, David; Turner, Carl Journal of High Energy Physics, Vol. 2018, Issue 7 https://doi.org/10.1007/JHEP07(2018)059	journal	July 2018
Nonsupersymmetric Dualities from Mirror Symmetry Kachru, Shamit; Mulligan, Michael; Torroba, Gonzalo Physical Review Letters, Vol. 118, Issue 1 https://doi.org/10.1103/PhysRevLett.118.011602	journal	January 2017
Level/rank duality and Chern-Simons-matter theories Hsin, Po-Shen; Seiberg, Nathan Journal of High Energy Physics, Vol. 2016, Issue 9 https://doi.org/10.1007/JHEP09(2016)095	journal	September 2016
Particle-vortex duality and the modular group: Applications to the quantum Hall effect and other two-dimensional systems Burgess, C. P.; Dolan, Brian P. Physical Review B, Vol. 63, Issue 15 https://doi.org/10.1103/PhysRevB.63.155309	journal	March 2001
Bosonization in arbitrary genus Alvarez-Gaumé, Luis; Moore, Gregory; Nelson, Philip Physics Letters B, Vol. 178, Issue 1 https://doi.org/10.1016/0370-2693(86)90466-1	journal	September 1986
Phase Transition in a Lattice Model of Superconductivity Dasgupta, C.; Halperin, B. I. Physical Review Letters, Vol. 47, Issue 21 https://doi.org/10.1103/PhysRevLett.47.1556	journal	November 1981
Flows, fixed points and duality in Chern-Simons-matter theories Aharony, Ofer; Jain, Sachin; Minwalla, Shiraz Journal of High Energy Physics, Vol. 2018, Issue 12 https://doi.org/10.1007/JHEP12(2018)058	journal	December 2018
Three-dimensional dualities with bosons and fermions Benini, Francesco Journal of High Energy Physics, Vol. 2018, Issue 2 https://doi.org/10.1007/JHEP02(2018)068	journal	February 2018
Particle-Vortex Duality from 3D Bosonization Karch, Andreas; Tong, David Physical Review X, Vol. 6, Issue 3 https://doi.org/10.1103/PhysRevX.6.031043	journal	September 2016
Spin structures in string theory Seiberg, N.; Witten, E. Nuclear Physics B, Vol. 276, Issue 2 https://doi.org/10.1016/0550-3213(86)90297-X	journal	October 1986
Mandelstam-'t Hooft duality in abelian lattice models Peskin, Michael E. Annals of Physics, Vol. 113, Issue 1 https://doi.org/10.1016/0003-4916(78)90252-X	journal	July 1978
On mirror symmetry in three dimensional Abelian gauge theories Kapustin, Anton; Strassler, Matthew J. Journal of High Energy Physics, Vol. 1999, Issue 04 https://doi.org/10.1088/1126-6708/1999/04/021	journal	April 1999

Similar Records

Majorana chain and Ising model - (non-invertible) translations, anomalies, and emanant symmetries

Journal Article · Fri Mar 01 00:00:00 EST 2024 · SciPost Physics · OSTI ID:1564290

Seiberg, Nathan; Shao, Shu-Heng

Duality defect of the monster CFT

Journal Article · Mon Jan 18 00:00:00 EST 2021 · Journal of Physics. A, Mathematical and Theoretical · OSTI ID:1564290

Lin, Ying-Hsuan; Shao, Shu-Heng

String correlators on $\text{AdS}_3$: Analytic structure and dual CFT

Journal Article · Tue Sep 06 00:00:00 EDT 2022 · SciPost Physics · OSTI ID:1564290

Dei, Andrea; Eberhardt, Lorenz

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Conformal field theory (CFT)
Dualities
Gauge theory
Global symmetries
Jordan-Wigner fermions/transformation
Quantum field theory (QFT)

Title: A web of 2d dualities: $${\bf Z}_2$$ gauge fields and Arf invariants

Citation Formats

References (53)

Similar Records

Related Subjects