Infinite Family of Integrable Sigma Models Using Auxiliary Fields

Ferko, Christian; Smith, Liam

doi:10.1103/PhysRevLett.133.131602

Title: Infinite Family of Integrable Sigma Models Using Auxiliary Fields

Journal Article · 25 September 2024 · Physical Review Letters

DOI: https://doi.org/10.1103/PhysRevLett.133.131602 · OSTI ID:2448128

;

We introduce a class of 2D sigma models which are parametrized by a function of one variable. In addition to the physical field $g$ , these models include an auxiliary field $v_{α}$ which mediates interactions in a prescribed way. We prove that every theory in this family is classically integrable, in that it possesses an infinite set of conserved charges in involution, which can be constructed from a Lax representation for the equations of motion. This class includes the principal chiral model (PCM) and all deformations of the PCM by functions of the energy-momentum tensor. Published by the American Physical Society 2024

View Journal Article

Cite

Export

Save

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0009999

OSTI ID:: 2448128

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 13 Vol. 133; ISSN 0031-9007; ISSN PRLTAO

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (45)

Review of AdS/CFT Integrability: An Overview Beisert, Niklas; Ahn, Changrim; Alday, Luis F. Letters in Mathematical Physics, Vol. 99, Issue 1-3 https://doi.org/10.1007/s11005-011-0529-2	journal	October 2011
Lax connections in -deformed integrable field theories * Chen, Bin; Hou, Jue; Tian, Jia Chinese Physics C, Vol. 45, Issue 9 https://doi.org/10.1088/1674-1137/ac0ee4	journal	September 2021
The Hamiltonian formalism and a many-valued analogue of Morse theory Novikov, S. P. Russian Mathematical Surveys, Vol. 37, Issue 5 https://doi.org/10.1070/RM1982v037n05ABEH004020	journal	October 1982
Non-abelian bosonization in two dimensions Witten, Edward Communications in Mathematical Physics, Vol. 92, Issue 4 https://doi.org/10.1007/BF01215276	journal	December 1984
Integrable interpolations: From exact CFTs to non-Abelian T-duals Sfetsos, Konstadinos Nuclear Physics B, Vol. 880 https://doi.org/10.1016/j.nuclphysb.2014.01.004	journal	March 2014
Superconformal duality-invariant models and $$ \mathcal{N} $$ = 4 SYM effective action Kuzenko, Sergei M. Journal of High Energy Physics, Vol. 2021, Issue 9 https://doi.org/10.1007/JHEP09(2021)180	journal	September 2021
Yang–Baxter deformations and generalized supergravity—a short summary Orlando, Domenico; Reffert, Susanne; Sakamoto, Jun-ichi Journal of Physics A: Mathematical and Theoretical, Vol. 53, Issue 44 https://doi.org/10.1088/1751-8121/abb510 443001	journal	October 2020
Hamiltonian structures for integrable classical theories from graded Kac-Moody algebras Maillet, Jean-Michel Physics Letters B, Vol. 167, Issue 4 https://doi.org/10.1016/0370-2693(86)91289-X	journal	February 1986
Counterterms vs. dualities Bossard, Guillaume; Nicolai, Hermann Journal of High Energy Physics, Vol. 2011, Issue 8 https://doi.org/10.1007/JHEP08(2011)074	journal	August 2011
Lorentz-invariant actions for chiral p -forms Pasti, Paolo; Sorokin, Dmitri; Tonin, Mario Physical Review D, Vol. 55, Issue 10 https://doi.org/10.1103/PhysRevD.55.6292	journal	May 1997
New approach to nonlinear electrodynamics: Dualities as symmetries of interaction Ivanov, E. A.; Zupnik, B. M. Physics of Atomic Nuclei, Vol. 67, Issue 12 https://doi.org/10.1134/1.1842299	journal	December 2004
Exact mass gap of the chiral SU(n)×SU(n) model Balog, J.; Naik, S.; Niedermayer, F. Physical Review Letters, Vol. 69, Issue 6 https://doi.org/10.1103/PhysRevLett.69.873	journal	August 1992
Duality-invariant nonlinear electrodynamics and stress tensor flows Ferko, Christian; Kuzenko, Sergei M.; Smith, Liam Physical Review D, Vol. 108, Issue 10 https://doi.org/10.1103/PhysRevD.108.106021	journal	November 2023
On space of integrable quantum field theories Smirnov, F. A.; Zamolodchikov, A. B. Nuclear Physics B, Vol. 915 https://doi.org/10.1016/j.nuclphysb.2016.12.014	journal	February 2017
The One-Dimensional Hubbard Model Essler, Fabian H. L.; Frahm, Holger; Göhmann, Frank Cambridge University Press https://doi.org/10.1017/CBO9780511534843	book	January 2009
Homogeneous Yang-Baxter deformations as undeformed yet twisted models Borsato, Riccardo; Driezen, Sibylle; Miramontes, J. Luis Journal of High Energy Physics, Vol. 2022, Issue 4 https://doi.org/10.1007/JHEP04(2022)053	journal	April 2022
Yang-Baxter σ-models and dS/AdS T-duality Klimcík, Ctirad Journal of High Energy Physics, Vol. 2002, Issue 12 https://doi.org/10.1088/1126-6708/2002/12/051	journal	December 2002
Duality symmetric actions with manifest space-time symmetries Pasti, Paolo; Sorokin, Dmitrij; Tonin, Mario Physical Review D, Vol. 52, Issue 8 https://doi.org/10.1103/PhysRevD.52.R4277	journal	October 1995
Root- TT¯ Deformations in Two-Dimensional Quantum Field Theories Ferko, Christian; Sfondrini, Alessandro; Smith, Liam Physical Review Letters, Vol. 129, Issue 20 https://doi.org/10.1103/PhysRevLett.129.201604	journal	November 2022
New integrable canonical structures in two-dimensional models Maillet, Jean-Michael Nuclear Physics B, Vol. 269, Issue 1 https://doi.org/10.1016/0550-3213(86)90365-2	journal	May 1986
Reliable Perturbative Results for Strong Interactions? Politzer, H. David Physical Review Letters, Vol. 30, Issue 26 https://doi.org/10.1103/PhysRevLett.30.1346	journal	June 1973
Marginal TT¯ -like deformation and modified Maxwell theories in two dimensions Babaei-Aghbolagh, H.; Babaei Velni, Komeil; Mahdavian Yekta, Davood Physical Review D, Vol. 106, Issue 8 https://doi.org/10.1103/PhysRevD.106.086022	journal	October 2022
T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ -deformed 2D quantum field theories Cavaglià, Andrea; Negro, Stefano; Szécsényi, István M. Journal of High Energy Physics, Vol. 2016, Issue 10 https://doi.org/10.1007/JHEP10(2016)112	journal	October 2016
Integrable deformations of sigma models Hoare, Ben Journal of Physics A: Mathematical and Theoretical, Vol. 55, Issue 9 https://doi.org/10.1088/1751-8121/ac4a1e	journal	February 2022
Brief lectures on duality, integrability and deformations Klimčík, Ctirad Reviews in Mathematical Physics, Vol. 33, Issue 06 https://doi.org/10.1142/S0129055X21300041	journal	June 2021
Classical integrability of root- TT¯ flows Borsato, Riccardo; Ferko, Christian; Sfondrini, Alessandro Physical Review D, Vol. 107, Issue 8 https://doi.org/10.1103/PhysRevD.107.086011	journal	April 2023
Jordanian deformations of the AdS5 × S5 superstring Kawaguchi, Io; Matsumoto, Takuya; Yoshida, Kentaroh Journal of High Energy Physics, Vol. 2014, Issue 4 https://doi.org/10.1007/JHEP04(2014)153	journal	April 2014
Foundations of the AdS ₅ × S ⁵ superstring: I Arutyunov, Gleb; Frolov, Sergey Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue 25 https://doi.org/10.1088/1751-8113/42/25/254003	journal	June 2009
Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model Haldane, F. D. M. Physics Letters A, Vol. 93, Issue 9 https://doi.org/10.1016/0375-9601(83)90631-X	journal	February 1983
Four-dimensional Chern–Simons theory and integrable field theories Lacroix, Sylvain Journal of Physics A: Mathematical and Theoretical, Vol. 55, Issue 8 https://doi.org/10.1088/1751-8121/ac48ed	journal	February 2022
Interacting chiral form field theories and $$ T\overline{T} $$-like flows in six and higher dimensions Ferko, Christian; Kuzenko, Sergei M.; Lechner, Kurt Journal of High Energy Physics, Vol. 2024, Issue 5 https://doi.org/10.1007/JHEP05(2024)320	journal	May 2024
Modave Lectures on Classical Integrability in 2d Field Theories Driezen, Sibylle Proceedings of Modave Summer School in Mathematical Physics — PoS(Modave2021) https://doi.org/10.22323/1.404.0002	conference	March 2022
On the origin of anomalies in the quantum non-local charge for the generalized non-linear sigma models Abdalla, E.; Gomes, M.; Forger, M. Nuclear Physics B, Vol. 210, Issue 2 https://doi.org/10.1016/0550-3213(82)90238-3	journal	September 1982
Flows in the space of interacting chiral boson theories Ebert, Stephen; Ferko, Christian; Martin, Cian Luke Physical Review D, Vol. 110, Issue 4 https://doi.org/10.1103/PhysRevD.110.046005	journal	August 2024
Bispinor auxiliary fields in duality-invariant electrodynamics revisited Ivanov, E. A.; Zupnik, B. M. Physical Review D, Vol. 87, Issue 6 https://doi.org/10.1103/PhysRevD.87.065023	journal	March 2013
Interaction of goldstone particles in two dimensions. Applications to ferromagnets and massive Yang-Mills fields Polyakov, A. M. Physics Letters B, Vol. 59, Issue 1 https://doi.org/10.1016/0370-2693(75)90161-6	journal	October 1975
Covariant action for a D = 11 five-brane with the chiral field Pasti, Paolo; Sorokin, Dmitri; Tonin, Mario Physics Letters B, Vol. 398, Issue 1-2 https://doi.org/10.1016/S0370-2693(97)00188-3	journal	April 1997
Emergence of non-linear electrodynamic theories from T T ¯ -like deformations Babaei-Aghbolagh, H.; Babaei Velni, Komeil; Yekta, Davood Mahdavian Physics Letters B, Vol. 829 https://doi.org/10.1016/j.physletb.2022.137079	journal	June 2022
Canonical quantisation of the gauged Wess-Zumino model Bowcock, P. Nuclear Physics B, Vol. 316, Issue 1 https://doi.org/10.1016/0550-3213(89)90387-8	journal	April 1989
On integrability of the Yang–Baxter σ-model Klimčík, Ctirad Journal of Mathematical Physics, Vol. 50, Issue 4 https://doi.org/10.1063/1.3116242	journal	April 2009
Nonlinear duality-invariant conformal extension of Maxwell’s equations Bandos, Igor; Lechner, Kurt; Sorokin, Dmitri Physical Review D, Vol. 102, Issue 12 https://doi.org/10.1103/PhysRevD.102.121703	journal	December 2020
Ultraviolet Behavior of Non-Abelian Gauge Theories Gross, David J.; Wilczek, Frank Physical Review Letters, Vol. 30, Issue 26 https://doi.org/10.1103/PhysRevLett.30.1343	journal	June 1973
$$ T\overline{T} $$ deformations in curved space from 4D Chern-Simons theory Py, Victor Journal of High Energy Physics, Vol. 2022, Issue 8 https://doi.org/10.1007/JHEP08(2022)101	journal	August 2022
On classical Yang-Baxter based deformations of the AdS5 × S5 superstring van Tongeren, Stijn J. Journal of High Energy Physics, Vol. 2015, Issue 6 https://doi.org/10.1007/JHEP06(2015)048	journal	June 2015
Consequences of anomalous ward identities Wess, J.; Zumino, B. Physics Letters B, Vol. 37, Issue 1 https://doi.org/10.1016/0370-2693(71)90582-X	journal	November 1971