Abstract
We study regularization scheme dependence of β-function for sigma models with two-dimensional target space. Working within four-loop approximation, we conjecture the scheme in which the β-function retains only two tensor structures up to certain terms containing ζ3. Using this scheme, we provide explicit solutions to RG flow equation corresponding to Yang-Baxter- and λ-deformed SU(2)/U(l) sigma models, for which these terms disappear.
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M. Kompaniets and E. Panzer, Renormalization group functions of ϕ4 theory in the MS-scheme to six loops, PoS LL2016 (2016) 038 [arXiv:1606.09210] [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, Regularization and renormalization of gauge fields, Nucl. Phys. B 44 (1972) 189 [INSPIRE].
G. ’t Hooft, Dimensional regularization and the renormalization group, Nucl. Phys. B 61 (1973) 455 [INSPIRE].
K.G. Wilson and J.B. Kogut, The renormalization group and the ϵ-expansion, Phys. Rept. 12 (1974) 75 [INSPIRE].
Y. Ilyashenko and S. Yakovenko, Lectures on analytic differential equations, American Mathematical Society, U.S.A. (2007).
A.B. Zamolodchikov, Mass scale in the sine-Gordon model and its reductions, Int. J. Mod. Phys. A 10 (1995) 1125 [INSPIRE].
B. Doyon and S.L. Lukyanov, Fermion Schwinger’s function for the SU(2)-Thirring model, Nucl. Phys. B 644 (2002) 451 [hep-th/0203135] [INSPIRE].
S.L. Lukyanov and V. Terras, Long distance asymptotics of spin spin correlation functions for the XXZ spin chain, Nucl. Phys. B 654 (2003) 323 [hep-th/0206093] [INSPIRE].
G. Ecker and J. Honerkamp, Application of invariant renormalization to the nonlinear chiral invariant pion lagrangian in the one-loop approximation, Nucl. Phys. B 35 (1971) 481 [INSPIRE].
D.H. Friedan, Nonlinear models in 2 + ϵ dimensions, Annals Phys. 163 (1985) 318 [INSPIRE].
S.J. Graham, Three loop β-function for the bosonic nonlinear σ model, Phys. Lett. B 197 (1987) 543 [INSPIRE].
A.P. Foakes and N. Mohammedi, Three loop calculation of the β-function for the purely metric nonlinear σ model, Phys. Lett. B 198 (1987) 359 [INSPIRE].
I. Jack, D.R.T. Jones and N. Mohammedi, A four loop calculation of the metric β-function for the bosonic σ model and the string effective action, Nucl. Phys. B 322 (1989) 431 [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Order α′ (two loop) equivalence of the string equations of motion and the sigma model Weyl invariance conditions: dependence on the dilaton and the antisymmetric tensor, Nucl. Phys. B 293 (1987) 385 [INSPIRE].
V. Fateev, Classical and quantum integrable sigma models. Ricci flow, “nice duality” and perturbed rational conformal field theories, J. Exp. Theor. Phys. 129 (2019) 566 [arXiv:1902.02811] [INSPIRE].
B. Hoare, N. Levine and A.A. Tseytlin, Integrable 2d sigma models: quantum corrections to geometry from RG flow, Nucl. Phys. B 949 (2019) 114798 [arXiv:1907.04737] [INSPIRE].
B. Hoare, N. Levine and A.A. Tseytlin, Integrable sigma models and 2-loop RG flow, JHEP 12 (2019) 146 [arXiv:1910.00397] [INSPIRE].
B. Hoare, N. Levine and A.A. Tseytlin, Sigma models with local couplings: a new integrability-RG flow connection, JHEP 11 (2020) 020 [arXiv:2008.01112] [INSPIRE].
N. Levine and A.A. Tseytlin, Integrability vs. RG flow in G × G and G × G/H sigma models, JHEP 05 (2021) 076 [arXiv:2103.10513] [INSPIRE].
V.A. Fateev, E. Onofri and A.B. Zamolodchikov, Integrable deformations of the O(3) sigma model. The sausage model, Nucl. Phys. B 406 (1993) 521 [INSPIRE].
K. Sfetsos, Integrable interpolations: from exact CFTs to non-Abelian T-duals, Nucl. Phys. B 880 (2014) 225 [arXiv:1312.4560] [INSPIRE].
T.J. Hollowood, J.L. Miramontes and D.M. Schmidtt, Integrable deformations of strings on symmetric spaces, JHEP 11 (2014) 009 [arXiv:1407.2840] [INSPIRE].
V.A. Fateev, Integrable deformations of sine-Liouville conformal field theory and duality, SIGMA 13 (2017) 080 [arXiv:1705.06424] [INSPIRE].
M.T. Grisaru, A.E.M. van de Ven and D. Zanon, Four loop β-function for the N = 1 and N = 2 supersymmetric nonlinear sigma model in two-dimensions, Phys. Lett. B 173 (1986) 423 [INSPIRE].
M.T. Grisaru, A.E.M. van de Ven and D. Zanon, Two-dimensional supersymmetric sigma models on Ricci flat Kähler manifolds are not finite, Nucl. Phys. B 277 (1986) 388 [INSPIRE].
M.T. Grisaru, D.I. Kazakov and D. Zanon, Five loop divergences for the N = 2 supersymmetric nonlinear σ model, Nucl. Phys. B 287 (1987) 189 [INSPIRE].
I. Jack, D.R.T. Jones and J. Panvel, Six loop divergences in the supersymmetric Kähler sigma model, Int. J. Mod. Phys. A 8 (1993) 2591 [hep-th/9311117] [INSPIRE].
R. Dijkgraaf, H.L. Verlinde and E.P. Verlinde, String propagation in a black hole geometry, Nucl. Phys. B 371 (1992) 269 [INSPIRE].
C. Klimčík, On integrability of the Yang-Baxter sigma-model, J. Math. Phys. 50 (2009) 043508 [arXiv:0802.3518] [INSPIRE].
F. Delduc, M. Magro and B. Vicedo, On classical q-deformations of integrable sigma-models, JHEP 11 (2013) 192 [arXiv:1308.3581] [INSPIRE].
G. Itsios, K. Sfetsos and K. Siampos, The all-loop non-Abelian Thirring model and its RG flow, Phys. Lett. B 733 (2014) 265 [arXiv:1404.3748] [INSPIRE].
C. Appadu and T.J. Hollowood, β-function of k deformed AdS5 × S5 string theory, JHEP 11 (2015) 095 [arXiv:1507.05420] [INSPIRE].
B. Hoare and A.A. Tseytlin, On integrable deformations of superstring sigma models related to AdSn × Sn supercosets, Nucl. Phys. B 897 (2015) 448 [arXiv:1504.07213] [INSPIRE].
A.V. Litvinov and L.A. Spodyneiko, On dual description of the deformed O(N) sigma model, JHEP 11 (2018) 139 [arXiv:1804.07084] [INSPIRE].
E. Witten, On string theory and black holes, Phys. Rev. D 44 (1991) 314 [INSPIRE].
I. Bars and K. Sfetsos, Conformally exact metric and dilaton in string theory on curved space-time, Phys. Rev. D 46 (1992) 4510 [hep-th/9206006] [INSPIRE].
M. Grigoriev and A.A. Tseytlin, Pohlmeyer reduction of AdS5 × S5 superstring sigma model, Nucl. Phys. B 800 (2008) 450 [arXiv:0711.0155] [INSPIRE].
S. Demulder, K. Sfetsos and D.C. Thompson, Integrable λ-deformations: squashing coset CFTs and AdS5 × S5, JHEP 07 (2015) 019 [arXiv:1504.02781] [INSPIRE].
M. Alfimov, B. Feigin, B. Hoare and A. Litvinov, Dual description of η-deformed OSP sigma models, JHEP 12 (2020) 040 [arXiv:2010.11927] [INSPIRE].
T. Nutma, xTras: a field-theory inspired xAct package for mathematica, Comput. Phys. Commun. 185 (2014) 1719 [arXiv:1308.3493] [INSPIRE].
D. Brizuela, J.M. Martin-Garcia and G.A. Mena Marugan, xPert: computer algebra for metric perturbation theory, Gen. Rel. Grav. 41 (2009) 2415 [arXiv:0807.0824] [INSPIRE].
T. Nutma, xTras: a field-theory inspired xAct package for mathematica, Comput. Phys. Commun. 185 (2014) 1719 [arXiv:1308.3493] [INSPIRE].
A. Litvinov and L. Spodyneiko, On W algebras commuting with a set of screenings, JHEP 11 (2016) 138 [arXiv:1609.06271] [INSPIRE].
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Alfimov, M., Litvinov, A. On loop corrections to integrable 2D sigma model backgrounds. J. High Energ. Phys. 2022, 43 (2022). https://doi.org/10.1007/JHEP01(2022)043
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DOI: https://doi.org/10.1007/JHEP01(2022)043