Work

Sign flip triangulations of the amplituhedron

Year: 2020

Type: article

Abstract: We present new triangulations of the m = 4 amplituhedron relevant for scattering amplitudes in planar $$ \mathcal{N} $$ N = 4 super-Yang-Mills, obtained directly from the combinatorial definition of the geometry. Using the “sign flip” characterization of the amplituhedron, we reproduce the canonical forms for the all-multiplicity next-to-maximally helicity violating (NMHV) and next-to-next-to-maximally helicity violating (N2MHV) tree-level as well as the NMHV one-loop cases, without using any input from traditional amplitudes methods. Our results provide strong evidence for the equivalence of the original definition of the amplituhedron [1] and the topological one [2], and suggest a new path forward for computing higher loop amplitudes geometrically. In particular, we realize the NMHV one-loop amplituhedron as the intersection of two amplituhedra of lower dimensionality, which is reflected in the novel structure of the corresponding canonical form.

Source: Journal of High Energy Physics

DOI: 10.1007/jhep05(2020)121

Authors: Ryota Kojima, Cameron Langer

Institutions: High Energy Accelerator Research Organization, The Graduate University for Advanced Studies, SOKENDAI, University of California, Davis

Language: English

Topic: Black Holes and Theoretical Physics

Subfield: Nuclear and High Energy Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funders: U.S. Department of Energy, Chinese Academy of Sciences, University of California, Davis

Award: HIGH ENERGY PARTICLE PHYSICS RESEARCH