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Published February 10, 2017 | Published
Journal Article Open

Generalized Wilson-Fisher Critical Points from the Conformal Operator Product Expansion


We study possible smooth deformations of the generalized free conformal field theory in arbitrary dimensions by exploiting the singularity structure of the conformal blocks dictated by the null states. We derive in this way, at the first nontrivial order in the ε expansion, the anomalous dimensions of an infinite class of scalar local operators, without using the equations of motion. In the cases where other computational methods apply, the results agree.

Additional Information

© 2017 American Physical Society. (Received 13 December 2016; revised manuscript received 10 January 2017; published 9 February 2017) Our work has been strongly inspired by some unpublished notes of Yu Nakayama on smooth deformations of the free-field theory in d = 6 − ε dimensions. We thank him for sharing with us his notes. We also thank M. Bianchi and D. Simmons-Duffin for helpful discussion. F. G. thanks the OIST of Okinawa where part of this work was done. The work of C. W. is supported by DOE Grant No. DE-SC0010255. A. C. P. thanks CPHT École Polytechnique, for its warm hospitality during the final stages of this work. The work of A. L. G. is funded under a CUniverse research promotion project by Chulalongkorn University (grant reference CUAASC).

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Published - PhysRevLett.118.061601.pdf


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August 19, 2023
August 19, 2023