Dimensional reduction for conformal blocks

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.