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

Chia-Kai Kuo* and Qinglin Yang†

  • *Contact author: chia-kai.kuo@mpp.mpg.de
  • †Contact author: qlyang@mpp.mpg.de
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Phys. Rev. D 113, 105022 – Published 26 May, 2026

DOI: https://doi.org/10.1103/61zh-vkhg

Abstract

We study five-point off-shell conformal integrals and the associated half-Bogomol’nyi–Prasad–Sommerfield (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 nonmaximal sectors.

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Phys. Rev. D 113, 105022– Published 26 May, 2026
  • Received 25 January 2026
  • Accepted 21 April 2026
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