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The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points

Gliozzi, Ferdinando and Guerrieri, Andrea L. and Petkou, Anastasios C. and Wen, Congkao (2017) The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points. Journal of High Energy Physics, 2017 (4). Art. No. 056. ISSN 1126-6708. doi:10.1007/JHEP04(2017)056.

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We describe in detail the method used in our previous work arXiv:1611.10344 to study the Wilson-Fisher critical points nearby generalized free CFTs, exploiting the analytic structure of conformal blocks as functions of the conformal dimension of the exchanged operator. Our method is equivalent to the mechanism of conformal multiplet recombination set up by null states. We compute, to the first non-trivial order in the ϵ-expansion, the anomalous dimensions and the OPE coefficients of infinite classes of scalar local operators using just CFT data. We study single-scalar and O(N)-invariant theories, as well as theories with multiple deformations. When available we agree with older results, but we also produce a wealth of new ones. Unitarity and crossing symmetry are not used in our approach and we are able to apply our method to non-unitary theories as well. Some implications of our results for the study of the non-unitary theories containing partially conserved higher-spin currents are briefly mentioned.

Item Type:Article
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Wen, Congkao0000-0002-5174-1576
Additional Information:© 2017 The Author(s). 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. Received: 22 February 2017; Accepted: 30 March 2017; First Online: 11 April 2017. A large part of this work was performed while A. C. P. was visiting CHPT at Ecole Polytechnique which he wishes to thank for the excellent hospitality extended to him. A. C. P. wishes also to thank X. Bekaert, K. Hinterbichler, P. M. Petropoulos, M. Picco, Z. Skvorstov, S. Sleight, M. Taronna and A. Tseytlin for useful discussions and correspondence. F. G. wishes to thank E. Brezin and S. Hikami for helpful discussions. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0010255. The work of A. C. P. is partially supported by the MPNS-COST Action MP1210 “The String Theory Universe”. The work of A. L. G. is funded under CUniverse research promotion project by Chulalongkorn University (grant reference CUAASC).
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0010255
MPNS-COST ActionMP1210
Chulalongkorn UniversityCUAASC
Subject Keywords:Conformal Field Theory; Higher Spin Symmetry
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Issue or Number:4
Record Number:CaltechAUTHORS:20170228-191103546
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Official Citation:Gliozzi, F., Guerrieri, A.L., Petkou, A.C. et al. J. High Energ. Phys. (2017) 2017: 56. doi:10.1007/JHEP04(2017)056
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:74621
Deposited By: Joy Painter
Deposited On:01 Mar 2017 03:59
Last Modified:11 Nov 2021 05:28

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