Perturbative gauge theory and 2+2=4

Abstract

The group $S_4$ of permutations on four elements has an irreducible representation corresponding to the partition 4=2+2. This representation appears in several different mathematical contexts: the Jacobi identity of Lie algebras; the Schouten identity for spinors; differences and the cross ratio in the projective plane; the Grassmannian space of 2-planes in linear algebra; the Riemann tensor in differential geometry; and more. We observe that all these occurrences are connected through perturbative non-abelian gauge theory, thereby acting as a leitmotif.

arXiv comment7 pages

References in corpus (7)

• Multi-Parton Amplitudes in Gauge Theories
• Scattering of Massless Particles in Arbitrary Dimension
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• The Grassmannian Origin Of Dual Superconformal Invariance
• Scattering Amplitudes
• Scattering amplitudes: the most perfect microscopic structures in the universe
• Color structures and permutations

Cited by in corpus (4)

• Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
• CHY representations for gauge theory and gravity amplitudes with up to three massive particles
• Scattering equations and virtuous kinematic numerators and dual-trace functions
• 1-loop Color structures and sunny diagrams