Year: 2014
Type: article
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” $ \mathbb{R} $ d+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.
Source: Journal of High Energy Physics
Author: David Simmons-Duffin
Institution: Harvard University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Funder: National Science Foundation
OpenAlex ID: W1973352851