Notes on off-shell conformal integrals and correlation functions at five points

TL;DR

This paper develops a basis of uniform-transcendental integrals for five-point off-shell conformal integrals in N=4 SYM, enabling explicit two-loop correlation function computations.

Contribution

It introduces a new basis of pure integrals for five-point conformal integrals, facilitating two-loop calculations in supersymmetric gauge theory.

Findings

Constructed a basis of six topologies of UT pure integrals.

Mapped the basis to known two-loop four-mass integral families.

Computed symbol-level results for two-loop five-point correlators.

Abstract

We study five-point off-shell conformal integrals and the associated half-BPS correlation functions at two loops in the 't Hooft coupling expansion of maximally supersymmetric Yang-Mills theory. We construct a basis of uniform-transcendental (UT) pure integrals spanning six distinct topologies by diagonalizing leading singularities subject to conformal invariance. By fixing conformal frames, this basis can be mapped to known two-loop four-mass integral families. We then compute the integrated results by combining canonical differential equations with integration-by-parts reduction. As an application, we present symbol-level integrated results for the two-loop five-point half-BPS correlators, including both maximal and non-maximal sectors.