A Compact Form of 3D Conformal Block

Abstract: We reveal an intriguing connection between conformal blocks and fractional calculus. By employing a modified form of half-derivates, we discover a compact representation of the three-dimensional conformal block, expressed as the product of two hypergeometric 4F3 functions. Furthermore, our method leads to several implications for two-dimensional Conformal Field Theory (CFT), which we explore towards the conclusion of this paper.