Abstract
We continue our study of λ-deformed σ-models by setting up a \( \frac{1}{k} \) perturbative expansion around the free field point for cosets, in particular for the λ-deformed SU(2)/U(1) coset CFT. We construct an interacting field theory in which all deformation effects are manifestly encoded in the interaction vertices. Using this we reproduce the known β-function and the anomalous dimension of the composite operator perturbing away from the conformal point. We introduce the λ-dressed parafermions which have an essential Wilson- like phase in their expressions. Subsequently, we compute their anomalous dimension, as well as their four-point functions, as exact functions of the deformation and to leading order in the k expansion. Correlation functions with an odd number of these parafermions vanish as in the conformal case.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
T.J. Hollowood, J. Miramontes and D.M. Schmidtt, An integrable deformation of the AdS5 × S5 superstring, J. Phys. A 47 (2014) 495402 [arXiv:1409.1538] [INSPIRE].
G. Georgiou and K. Sfetsos, A new class of integrable deformations of CFTs, JHEP 03 (2017) 083 [arXiv:1612.05012] [INSPIRE].
G. Georgiou and K. Sfetsos, Integrable flows between exact CFTs, JHEP 11 (2017) 078 [arXiv:1707.05149] [INSPIRE].
K. Sfetsos and K. Siampos, Integrable deformations of the \( {G}_{k_1} \) × \( {G}_{k_2}/{G}_{k_1}{+}_{k_2} \) coset CFTs, Nucl. Phys. B 927 (2018) 124 [arXiv:1710.02515] [INSPIRE].
K. Sfetsos, K. Siampos and D.C. Thompson, Generalised integrable λ- and η-deformations and their relation, Nucl. Phys. B 899 (2015) 489 [arXiv:1506.05784] [INSPIRE].
G. Georgiou and K. Sfetsos, Novel all loop actions of interacting CFTs: Construction, integrability and RG flows, Nucl. Phys. B 937 (2018) 371 [arXiv:1809.03522] [INSPIRE].
G. Georgiou and K. Sfetsos, The most general λ-deformation of CFTs and integrability, JHEP 03 (2019) 094 [arXiv:1812.04033] [INSPIRE].
S. Driezen, A. Sevrin and D.C. Thompson, Integrable asymmetric λ-deformations, JHEP 04 (2019) 094 [arXiv:1902.04142] [INSPIRE].
D. Kutasov, String theory and the nonabelian Thirring model, Phys. Lett. B 227 (1989) 68 [INSPIRE].
B. Gerganov, A. LeClair and M. Moriconi, On the β-function for anisotropic current interactions in 2D, Phys. Rev. Lett. 86 (2001) 4753 [hep-th/0011189] [INSPIRE].
D. Kutasov, Duality off the critical point in two-dimensional systems with nonabelian symmetries, Phys. Lett. B 233 (1989) 369 [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].
K. Sfetsos and K. Siampos, Gauged WZW-type theories and the all-loop anisotropic non-Abelian Thirring model, Nucl. Phys. B 885 (2014) 583 [arXiv:1405.7803] [INSPIRE].
C. Appadu and T.J. Hollowood, β-function of k deformed AdS5 × S5 string theory, JHEP 11 (2015) 095 [arXiv:1507.05420] [INSPIRE].
E. Sagkrioti, K. Sfetsos and K. Siampos, RG flows for λ-deformed CFTs, Nucl. Phys. B 930 (2018) 499 [arXiv:1801.10174] [INSPIRE].
G. Georgiou, K. Sfetsos and K. Siampos, All-loop anomalous dimensions in integrable λ-deformed σ-models, Nucl. Phys. B 901 (2015) 40 [arXiv:1509.02946] [INSPIRE].
G. Georgiou, P. Panopoulos, E. Sagkrioti and K. Sfetsos, Exact results from the geometry of couplings and the effective action, Nucl. Phys. B 948 (2019) 114779 [arXiv:1906.00984] [INSPIRE].
G. Georgiou, P. Panopoulos, E. Sagkrioti, K. Sfetsos and K. Siampos, The exact C -function in integrable λ-deformed theories, Phys. Lett. B 782 (2018) 613 [arXiv:1805.03731] [INSPIRE].
E. Sagkrioti, K. Sfetsos and K. Siampos, Weyl anomaly and the C -function in λ-deformed CFTs, Nucl. Phys. B 938 (2019) 426 [arXiv:1810.04189] [INSPIRE].
G. Georgiou, K. Sfetsos and K. Siampos, All-loop correlators of integrable λ-deformed σ-models, Nucl. Phys. B 909 (2016) 360 [arXiv:1604.08212] [INSPIRE].
G. Georgiou, K. Sfetsos and K. Siampos, λ-deformations of left-right asymmetric CFTs, Nucl. Phys. B 914 (2017) 623 [arXiv:1610.05314] [INSPIRE].
G. Georgiou, K. Sfetsos and K. Siampos, Double and cyclic λ-deformations and their canonical equivalents, Phys. Lett. B 771 (2017) 576 [arXiv:1704.07834] [INSPIRE].
G. Georgiou, E. Sagkrioti, K. Sfetsos and K. Siampos, Quantum aspects of doubly deformed CFTs, Nucl. Phys. B 919 (2017) 504 [arXiv:1703.00462] [INSPIRE].
G. Georgiou and K. Sfetsos, Field theory and λ-deformations: expanding around the identity, Nucl. Phys. B 950 (2020) 114855 [arXiv:1910.01056] [INSPIRE].
V.A. Fateev and A.B. Zamolodchikov, Parafermionic currents in the two-dimensional conformal quantum field theory and selfdual critical points in Z (n) invariant statistical systems, Sov. Phys. JETP 62 (1985) 215 [INSPIRE].
G. Georgiou, E. Sagkrioti, K. Sfetsos and K. Siampos, An exact symmetry in λ-deformed CFTs, JHEP 01 (2020) 083 [arXiv:1911.02027] [INSPIRE].
P. Bowcock, Canonical Quantization of the Gauged Wess-Zumino Model, Nucl. Phys. B 316 (1989) 80 [INSPIRE].
K. Bardakci, M.J. Crescimanno and E. Rabinovici, Parafermions from coset models, Nucl. Phys. B 344 (1990) 344 [INSPIRE].
K. Bardakci, M.J. Crescimanno and S. Hotes, Parafermions from nonabelian coset models, Nucl. Phys. B 349 (1991) 439 [INSPIRE].
O. Lunin and W. Tian, Analytical structure of the generalized λ-deformation, Nucl. Phys. B 929 (2018) 330 [arXiv:1711.02735] [INSPIRE].
S. Demulder, F. Hassler, G. Piccinini and D.C. Thompson, Integrable deformation of ℂℙn and generalised Kähler geometry, arXiv:2002.11144 [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
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2004.10216
Rights and permissions
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.
About this article
Cite this article
Georgiou, G., Sfetsos, K. & Siampos, K. A free field perspective of λ-deformed coset CFT’s. J. High Energ. Phys. 2020, 187 (2020). https://doi.org/10.1007/JHEP07(2020)187
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2020)187