Conformal Blocks for the 4-Point Function in Conformal Quantum Mechanics

TL;DR

This paper analyzes the conformal block structure of four-point functions in conformal quantum mechanics, revealing that only one conformal block contributes and exploring the properties of the involved states.

Contribution

It extends previous work to four-point functions in conformal quantum mechanics, identifying the conformal block structure and constructing the dynamical evolution.

Findings

Only one conformal block contributes to the four-point function.

Conformal covariance is maintained despite non-primary operators.

Dynamical evolution is generated by the compact SO(2,1) generator.

Abstract

Extending previous work on 2 -- and 3 -- point functions, we study the 4 -- point function and its conformal block structure in conformal quantum mechanics CFT$_1$, 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).