Dimensional Reduction for Conformal Blocks
arXiv:1604.08913 · doi:10.1007/JHEP09(2016)017
Abstract
We consider the dimensional reduction of a CFT, breaking multiplets of the d-dimensional conformal group SO(d+1,1) up into multiplets of SO(d,1). This leads to an expansion of d-dimensional conformal blocks in terms of blocks in d-1 dimensions. In particular, we obtain a formula for 3d conformal blocks as an infinite sum over 2F1 hypergeometric functions with closed-form coefficients.
12 pages, 1 figure