Antipodal Self-Duality for a Four-Particle Form Factor

TL;DR

This paper computes the two-loop four-particle form factor in planar N=4 super-Yang-Mills theory, revealing a unique antipodal self-duality property of its remainder function related to symbol structure and symmetries.

Contribution

It introduces the first bootstrap of the four-particle form factor symbol, demonstrating antipodal self-duality and extended Steinmann relations in this context.

Findings

The symbol involves only 34 letters and obeys extended Steinmann relations.

The remainder function exhibits antipodal self-duality under a combined map.

Self-duality connects the three-particle form factor and six-particle amplitude.

Abstract

We bootstrap the symbol of the maximal-helicity-violating four-particle form factor for the chiral part of the stress-tensor supermultiplet in planar $\mathcal{N}=4$ super-Yang-Mills theory at two loops. When minimally normalized, this symbol involves only 34 letters and obeys the extended Steinmann relations in all partially-overlapping three-particle momentum channels. In addition, the remainder function for this form factor exhibits an antipodal self-duality: it is invariant under the combined operation of the antipodal map defined on multiple polylogarithms -- which reverses the order of the symbol letters -- and a simple kinematic map. This self-duality holds on a four-dimensional parity-preserving kinematic hypersurface. It implies the antipodal duality recently noticed between the three-particle form factor and the six-particle amplitude in this theory.