Leading singularities and off-shell conformal integrals

Understand

The three-loop four-point function of stress-tensor multiplets in N=4 super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals.

• In this paper we evaluate the unknown integrals, thus obtaining the three-loop correlation function analytically.
• The integrals have the generic structure of rational functions multiplied by (multiple) polylogarithms.
• We use the idea of leading singularities to obtain the rational coefficients, the symbol - with an appropriate ansatz for its structure - as a means of characterising multiple polylogarithms, and the technique of asymptotic expansion of Feynman integrals to obtain the integrals in certain limits.