Unwinding the amplituhedron in binary

By N. Arkani-Hamed, Hugh Thomas, J. Trnka. 2017

137 citations recorded by the source corpus.

A bstractWe present new, fundamentally combinatorial and topological characterizations of the amplituhedron. Upon projecting external data through the amplituhedron, the resulting configuration of points has a specified (and maximal) generalized “winding number”. Equivalently, the amplituhedron can be fully described in binary: canonical projections of the geometry down to one dimension have a specified (and maximal) number of “sign flips” of the projected data. The locality and unitarity of scattering amplitudes are easily derived as elementary consequences of this binary code. Minimal winding defines a natural “dual” of the amplituhedron. This picture gives us an avatar of the amplituhedron purely in the configuration space of points in vector space (momentum-twistor space in the physics), a new interpretation of the canonical amplituhedron form, and a direct bosonic understanding of the scattering super-amplitude in planar N$$ \mathcal{N} $$ = 4 SYM as a differential form on the space of physical kinematical data.

Subfields: Materials Chemistry, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5a047ee5aa4ef578b79d08c687c429d47290b0b5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Nuclear and High Energy Physics

1. Yuntao Bai
2. N. Arkani-Hamed
3. Song He
4. Gongwang Yan
5. F. Cachazo
6. C. Cheung
7. I. Low
8. Claudia de Rham

In Statistical and Nonlinear Physics

1. Yuntao Bai
2. N. Arkani-Hamed
3. Gongwang Yan
4. Song He
5. F. Cachazo
6. E. Pajer
7. Eran Palti
8. C. Cheung

Citations in the corpus

• Scattering forms and the positive geometry of kinematics, color and the worldsheet (2017, background): “Furthermore, there is a striking similarity between this description of bi-adjoint φ3 scattering amplitudes and the description of planarN = 4 super Yang-Mills (SYM) with the amplituhedron as the positive geometry [14].”
• The cosmological bootstrap: inflationary correlators from symmetries and singularities (2018, unknown): “Indeed, even some first hints for such a description, seen in perturbation theory, involve much more alien combinatorial, geometric and number-theoretic ideas [9–16], from which the physics of spacetime and quantum mechanics—locality and unitarity—emerge as derivative notions, with a huge amount lef”