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Projectors, shadows, and conformal blocks

Simmons-Duffin, David (2014) Projectors, shadows, and conformal blocks. Journal of High Energy Physics, 2014 (4). Art. no. 146. ISSN 1029-8479. https://resolver.caltech.edu/CaltechAUTHORS:20170815-121618494

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Abstract

We introduce a method for computing conformal blocks of operators in arbitrary Lorentz representations in any spacetime dimension, making it possible to apply bootstrap techniques to operators with spin. The key idea is to implement the “shadow formalism” of Ferrara, Gatto, Grillo, and Parisi in a setting where conformal invariance is manifest. Conformal blocks in d-dimensions can be expressed as integrals over the projective null-cone in the “embedding space” R^(Rd+1,1). Taking care with their analytic structure, these integrals can be evaluated in great generality, reducing the computation of conformal blocks to a bookkeeping exercise. To facilitate calculations in four-dimensional CFTs, we introduce techniques for writing down conformally-invariant correlators using auxiliary twistor variables, and demonstrate their use in some simple examples.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/JHEP04(2014)146DOIArticle
https://link.springer.com/article/10.1007/JHEP04(2014)146#Abs1PublisherArticle
https://arxiv.org/abs/1204.3894arXivDiscussion Paper
ORCID:
AuthorORCID
Simmons-Duffin, David0000-0002-2937-9515
Additional Information:© The Author(s) 2014. Received: February 12, 2014 Accepted: March 17, 2014 Published: April 24, 2014 I am grateful to J. Bourjaily, C. Córdova, R. Loganayagam, D. Poland, S. Raju, and S. Rychkov for discussions and comments. This work is supported by NSF grant PHY-0855591 and the Harvard Center for the Fundamental Laws of Nature. 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
Funders:
Funding AgencyGrant Number
NSFPHY-0855591
Harvard Center for the Fundamental Laws of NatureUNSPECIFIED
Subject Keywords:Conformal and W Symmetry, Differential and Algebraic Geometry
Issue or Number:4
Record Number:CaltechAUTHORS:20170815-121618494
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170815-121618494
Official Citation:Simmons-Duffin, D. J. High Energ. Phys. (2014) 2014: 146. https://doi.org/10.1007/JHEP04(2014)146
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80419
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:16 Aug 2017 22:47
Last Modified:03 Oct 2019 18:30

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