Conformal basis, optical theorem, and the bulk point singularity
Conformal basis, optical theorem, and the bulk point singularity
复制标题
共形基、光学定理和体点奇点
作者：
Ho Tat Lam;Shu
我们研究了共形基的一般性质，在$（d+2）$维Minkowski空间的波函数空间是洛伦兹群$SO（1，d+1）$的原色。在这个基础上写的散射振幅具有相同的对称性$d$维共形算子。我们把光学定理，这是一个直接后果的幺正性，到共形的基础。在树级交换图的特殊情况下，光学定理采用主连续级数上的保角块分解的形式，OPE系数是写在同一基上的三点耦合。进一步讨论了AdS/CFT中无质量共形基与体点奇异性之间的关系。在此基础上，我们计算了（2+1）维中的三点和四点振幅，以证明这些结果。
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.