Conformal four-point ladder integrals in diverse dimensions and polylogarithms

A bstract In the paper, a family of conformal four-point ladder diagrams in arbitrary space-time dimensions is considered. We use the representation obtained via explicit calculation using the operator approach and conformal quantum mechanics to study their properties such as symmetries, loop and dimensional shift identities. In even dimensions, latter allows one to reduce the problem to the two-dimensional case, where notable factorization holds. Additionally, for a specific choice of propagator powers, we show that the representation can be written in the form of linear combinations of classical polylogarithms (with coefficients that are rational functions) and explore the structure of the resulting expressions.