Conformal Field Theory and Functions of Hypergeometric Type

Abstract

Conformal field theory provides a universal description of v arious phenomena in natural sciences. Its development, swift and successful, belongs to the major hig hlights of theoretical physics of the late XX century. In contrast, advances of the theory of hypergeomet ric functions always assumed a slower pace throughout the centuries of its existence. Functional iden tities studied by this mathematical discipline are fascinating both in their complexity and beauty. This thesi s investigates the interrelation of two subjects through a direct analysis of three CFT problems: two-point f unctions of the 2d strange metal CFT, three- point functions of primaries of the non-rational Toda CFT an d kinematical parts of Mellin amplitudes for scalar four-point functions in general dimensions. We flash out various generalizations of hypergeometric functions as a natural mathematical language for two of thes e problems. Several new methods inspired by extensions of classical results on hypergeometric funct ions, are presented. This work is based on our publications [1–3] as well as on one paper at the final stage of preparation [4].