Conformal Partial Waves: Further Mathematical Results

Understand

Further results for conformal partial waves for four point functions for conformal primary scalar fields in conformally invariant theories are obtained.

• They are defined as eigenfunctions of the differential Casimir operators for the conformal group acting on two variable functions subject to appropriate boundary conditions.
• As well as the scale dimension $\Delta$ and spin $\ell$ the conformal partial waves depend on two parameters $a,b$ related to the dimensions of the operators in the four point function.
• Expressions for the Mellin transform of conformal partial waves are obtained in terms of polynomials of the Mellin transform variables given in terms of finite sums.