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arXiv · 1711.06138

Conformal Basis, Optical Theorem, and the Bulk Point Singularity

Ho Tat Lam·Shu-Heng Shao
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Abstract

We study general properties of the conformal basis, the space of wavefunctions in $(d+2)$-dimensional Minkowski space that are primaries of the Lorentz group $SO(1,d+1)$. Scattering amplitudes written in this basis have the same symmetry as $d$-dimensional conformal correlators. We translate the optical theorem, which is a direct consequence of unitarity, into the conformal basis. In the particular case of a tree-level exchange diagram, the optical theorem takes the form of a conformal block decomposition on the principal continuous series, with OPE coefficients being the three-point coupling written in the same basis. We further discuss the relation between the massless conformal basis and the bulk point singularity in AdS/CFT. Some three- and four-point amplitudes in (2+1) dimensions are explicitly computed in this basis to demonstrate these results.

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Ho Tat Lam, Shu-Heng Shao. 2017-11-16. Conformal Basis, Optical Theorem, and the Bulk Point Singularity. https://doi.org/10.1103/physrevd.98.025020

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