Conformal blocks for the four-point function in conformal quantum mechanics

Abstract

Extending previous work on two- and three-point functions, we study the four-point function and its conformal block structure in conformal quantum mechanics CFT[subscript 1], which realizes the SO(2,1) symmetry group. Conformal covariance is preserved even though the operators with which we work need not be primary and the states are not conformally invariant. We find that only one conformal block contributes to the four-point function. We describe some further properties of the states that we use and we construct dynamical evolution generated by the compact generator of SO(2,1).