Abstract
We introduce and study conformal field theories specified by W −algebras commuting with certain set of screening charges. These CFT’s possess perturbations which define integrable QFT’s. We establish that these QFT’s have local and non-local Integrals of Motion and admit the perturbation theory in the weak coupling region. We construct factorized scattering theory which is consistent with non-local Integrals of Motion and perturbation theory. In the strong coupling limit the S−matrix of this QFT tends to the scattering matrix of the O(N) sigma model. The perturbation theory, Bethe ansatz technique, renormalization group approach and methods of conformal field theory are applied to show, that the constructed QFT’s are dual to integrable deformation of O(N) sigma-models.
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References
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].
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].
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, Integrable deformations of sine-Liouville conformal field theory and duality, SIGMA 13 (2017) 080 [arXiv:1705.0642].
V.A. Fateev, The Duality between two-dimensional integrable field theories and σ-models, Phys. Lett. B 357 (1995) 397 [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].
D.H. Friedan, Nonlinear models in 2 + ϵ dimensions, Annals Phys. 163 (1985) 318 [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].
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].
V.V. Bazhanov, Trigonometric solution of triangle equations and classical Lie algebras, Phys. Lett. 159B (1985) 321 [INSPIRE].
V.A. Fateev, The Exact relations between the coupling constants and the masses of particles for the integrable perturbed conformal field theories, Phys. Lett. B 324 (1994) 45 [INSPIRE].
A.B. Zamolodchikov, Mass scale in the sine-Gordon model and its reductions, Int. J. Mod. Phys. A 10 (1995) 1125 [INSPIRE].
M.P. Ganin, On a Fredholm integral equation whose kernel depends on the difference of the arguments, Izv. Vyssh. Uchebn. Zaved. Mat. 2 (1963) 31.
P. Hasenfratz and F. Niedermayer, The exact mass gap of the O(N) σ-model for arbitrary N ≥3 in d = 2, Phys. Lett. B 245 (1990) 529 [INSPIRE].
G. Perelman, The entropy formula for the Ricci flow and its geometric applications, math/0211159 [INSPIRE].
G. Arutyunov, R. Borsato and S. Frolov, S-matrix for strings on η-deformed AdS5 x S5, JHEP 04 (2014) 002 [arXiv:1312.3542] [INSPIRE].
B. Hoare and A. A. Tseytlin, On integrable deformations of superstring sigma models related to AdS n × S n supercosets, Nucl. Phys. B 897 (2015) 448 [arXiv:1504.0721].
C.-R. Ahn et al., Reflection amplitudes in nonsimply laced Toda theories and thermodynamic Bethe ansatz, Phys. Lett. B 481 (2000) 114 [hep-th/0002213] [INSPIRE].
D. Altschuler, Quantum equivalence of coset space models, Nucl. Phys. B 313 (1989) 293 [INSPIRE].
S.L. Lukyanov and V.A. Fateev, Exactly solvable models of conformal quantum theory associated with simple Lie algebra D(N ) (in Russian), Sov. J. Nucl. Phys. 49 (1989) 925 [INSPIRE].
V.A. Fateev and S.L. Lukyanov, Additional symmetries and exactly soluble models in two-dimensional conformal field theory, Sov. Sci. Rev. A 15 (1990) 1.
V.A. Fateev, Integrable deformations in Z(N) symmetrical models of conformal quantum field theory, Int. J. Mod. Phys. A 6 (1991) 2109 [INSPIRE].
V.A. Fateev and A.B. Zamolodchikov, Integrable perturbations of Z(N) parafermion models and O(3) σ-model, Phys. Lett. B 271 (1991) 91 [INSPIRE].
P. Fendley, σ-models as perturbed conformal field theories, Phys. Rev. Lett. 83 (1999) 4468 [hep-th/9906036] [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].
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ArXiv ePrint: 1804.03399
Dedicated to the memory of Lev Lipatov
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Fateev, V.A., Litvinov, A.V. Integrability, duality and sigma models. J. High Energ. Phys. 2018, 204 (2018). https://doi.org/10.1007/JHEP11(2018)204
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DOI: https://doi.org/10.1007/JHEP11(2018)204