Projectors, shadows, and conformal blocks
- Creators
- Simmons-Duffin, David
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.
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 creditedAttached Files
Published - 10.1007_2FJHEP04_2014_146.pdf
Submitted - 1204.3894.pdf
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Additional details
- Eprint ID
- 80419
- Resolver ID
- CaltechAUTHORS:20170815-121618494
- PHY-0855591
- NSF
- Harvard Center for the Fundamental Laws of Nature
- Created
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2017-08-16Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field