Two-loop D-dimensional unitarity and dual conformal symmetry

TL;DR

This paper explores how dual conformal symmetry influences Feynman integrals in dimensional regularization, revealing new relations and symmetries that extend beyond four dimensions, including nonplanar cases.

Contribution

It uncovers the application of dual conformal symmetry to D-dimensional Feynman integrals, including nonplanar analogs, and derives IBP relations without doubled propagators.

Findings

Dual conformal symmetry preserves unitarity cut surfaces outside 4D.

Differential equations have RHS proportional to (d-4) with no doubled propagators.

Identification of a nonplanar analog of dual conformal symmetry.

Abstract

In this talk we show that dual conformal symmetry has unexpected applications to Feynman integrals in dimensional regularization. Outside $4$ dimensions, the symmetry is anomalous, but still preserves the unitarity cut surfaces. This generally leads to differential equations whose RHS is proportional to $(d-4)$ and has no doubled propagators. The stabilizer subgroup of the conformal group leads to integration-by-parts (IBP) relations without doubled propagators. The above picture also suggested hints that led us to find a nonplanar analog of dual conformal symmetry.