Abstract
We study dual strong coupling description of integrability-preserving deformation of the O(N) sigma model. Dual theory is described by a coupled theory of Dirac fermions with four-fermion interaction and bosonic fields with exponential interactions. We claim that both theories share the same integrable structure and coincide as quantum field theories. We construct a solution of Ricci flow equation which behaves in the UV as a free theory perturbed by graviton operators and show that it coincides with the metric of the η-deformed O(N) sigma-model after T -duality transformation.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.R. Coleman, The Quantum sine-Gordon Equation as the Massive Thirring Model, Phys. Rev. D 11 (1975) 2088 [INSPIRE].
S. Mandelstam, Soliton Operators for the Quantized sine-Gordon Equation, Phys. Rev. D 11 (1975) 3026 [INSPIRE].
C. Klimčík, On integrability of the Yang-Baxter σ-model, J. Math. Phys. 50 (2009) 043508 [arXiv:0802.3518] [INSPIRE].
F. Delduc, M. Magro and B. Vicedo, On classical q-deformations of integrable σ-models, JHEP 11 (2013) 192 [arXiv:1308.3581] [INSPIRE].
V.A. Fateev and A.V. Litvinov, Integrability, Duality and σ-models, arXiv:1804.03399 [INSPIRE].
V.E. Zakharov and A.V. Mikhailov, Relativistically Invariant Two-Dimensional Models in Field Theory Integrable by the Inverse Problem Technique (in Russian), Sov. Phys. JETP 47 (1978) 1017 [INSPIRE].
A.M. Polyakov and P.B. Wiegmann, Theory of Nonabelian Goldstone Bosons, Phys. Lett. B 131 (1983) 121 [INSPIRE].
L.D. Faddeev, E.K. Sklyanin and L.A. Takhtajan, The Quantum Inverse Problem Method. 1, Theor. Math. Phys. 40 (1980) 688 [INSPIRE].
V.V. Bazhanov, G.A. Kotousov and S.L. Lukyanov, Quantum transfer-matrices for the sausage model, JHEP 01 (2018) 021 [arXiv:1706.09941] [INSPIRE].
A.M. Polyakov, Hidden Symmetry of the Two-Dimensional Chiral Fields, Phys. Lett. B 72 (1977) 224 [INSPIRE].
A.M. Polyakov, Interaction of Goldstone Particles in Two-Dimensions. Applications to Ferromagnets and Massive Yang-Mills Fields, Phys. Lett. B 59 (1975) 79 [INSPIRE].
E. Brézin and J. Zinn-Justin, Renormalization of the nonlinear σ-model in 2 + \( \epsilon \) dimensions. Application to the Heisenberg ferromagnets, Phys. Rev. Lett. 36 (1976) 691 [INSPIRE].
A.B. Zamolodchikov and A.B. Zamolodchikov, Factorized s Matrices in Two-Dimensions as the Exact Solutions of Certain Relativistic Quantum Field Models, Annals Phys. 120 (1979) 253 [INSPIRE].
A.B. Zamolodchikov and V.A. Fateev, Model factorized S matrix and an integrable Heisenberg chain with spin 1 (in Russian), Sov. J. Nucl. Phys. 32 (1980) 298 [INSPIRE].
M. Jimbo, Quantum r Matrix for the Generalized Toda System, Commun. Math. Phys. 102 (1986) 537 [INSPIRE].
V.V. Bazhanov, Trigonometric Solution of Triangle Equations and Classical Lie Algebras, Phys. Lett. B 159 (1985) 321 [INSPIRE].
D.H. Friedan, Nonlinear Models in 2 + \( \epsilon \) Dimensions, Annals Phys. 163 (1985) 318 [INSPIRE].
V.A. Fateev, E. Onofri and A.B. Zamolodchikov, The Sausage model (integrable deformations of O(3) σ-model), Nucl. Phys. B 406 (1993) 521 [INSPIRE].
S.L. Lukyanov, The integrable harmonic map problem versus Ricci flow, Nucl. Phys. B 865 (2012) 308 [arXiv:1205.3201] [INSPIRE].
B. Hoare, R. Roiban and A.A. Tseytlin, On deformations of AdS n × S n supercosets, JHEP 06 (2014) 002 [arXiv:1403.5517] [INSPIRE].
V.A. Fateev, Integrable Deformations of Sine-Liouville Conformal Field Theory and Duality, SIGMA 13 (2017) 080 [arXiv:1705.06424] [INSPIRE].
A. Litvinov and L. Spodyneiko, On W algebras commuting with a set of screenings, JHEP 11 (2016) 138 [arXiv:1609.06271] [INSPIRE].
C. Klimčík, Integrability of the bi-Yang-Baxter σ-model, Lett. Math. Phys. 104 (2014) 1095 [arXiv:1402.2105] [INSPIRE].
V.A. Fateev, The σ-model (dual) representation for a two-parameter family of integrable quantum field theories, Nucl. Phys. B 473 (1996) 509 [INSPIRE].
P. Goddard, A. Kent and D.I. Olive, Unitary Representations of the Virasoro and Supervirasoro Algebras, Commun. Math. Phys. 103 (1986) 105 [INSPIRE].
M. Goulian and M. Li, Correlation functions in Liouville theory, Phys. Rev. Lett. 66 (1991) 2051 [INSPIRE].
P. Baseilhac and V.A. Fateev, Expectation values of local fields for a two-parameter family of integrable models and related perturbed conformal field theories, Nucl. Phys. B 532 (1998) 567 [hep-th/9906010] [INSPIRE].
V.A. Fateev and A.V. Litvinov, Multipoint correlation functions in Liouville field theory and minimal Liouville gravity, Theor. Math. Phys. 154 (2008) 454 [arXiv:0707.1664] [INSPIRE].
V.V. Bazhanov and S.L. Lukyanov, Integrable structure of Quantum Field Theory: Classical flat connections versus quantum stationary states, JHEP 09 (2014) 147 [arXiv:1310.4390] [INSPIRE].
B. Hoare and A.A. Tseytlin, On integrable deformations of superstring σ-models related to AdS n × S n supercosets, Nucl. Phys. B 897 (2015) 448 [arXiv:1504.07213] [INSPIRE].
G. Arutyunov, R. Borsato and S. Frolov, S-matrix for strings on η-deformed AdS 5 × S 5, JHEP 04 (2014) 002 [arXiv:1312.3542] [INSPIRE].
S.L. Lukyanov and A.B. Zamolodchikov, Integrable circular brane model and Coulomb charging at large conduction, J. Stat. Mech. 0405 (2004) P05003 [hep-th/0306188] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1804.07084
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Litvinov, A.V., Spodyneiko, L.A. On dual description of the deformed O(N) sigma model. J. High Energ. Phys. 2018, 139 (2018). https://doi.org/10.1007/JHEP11(2018)139
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2018)139