The Scattering Variety
arXiv:1403.6833 · doi:10.1007/JHEP10(2014)135
Abstract
The so-called Scattering Equations which govern the kinematics of the scattering of massless particles in arbitrary dimensions have recently been cast into a system of homogeneous polynomials. We study these as affine and projective geometries which we call Scattering Varieties by analyzing such properties as Hilbert series, Euler characteristic and singularities. Interestingly, we find structures such as affine Calabi-Yau threefolds as well as singular K3 and Fano varieties.
29 pages; v2: substantially improved presentation, results added (Hodge diamond), references added, typos corrected
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Cited by in corpus (16)
- Aspects of Scattering Amplitudes and Moduli Space Localization
- 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
- Cross-ratio Identities and Higher-order Poles of CHY-integrand
- An Algebraic Approach to the Scattering Equations
- Scattering equations and virtuous kinematic numerators and dual-trace functions
- Elimination and recursions in the scattering equations
- Relations for Einstein-Yang-Mills amplitudes from the CHY representation
- General Solution of the Scattering Equations
- Scattering Equations: Real Solutions and Particles on a Line
- Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes
- The Role of Möbius Constants and Scattering Functions in CHY Scalar Amplitudes
- The CHY representation of tree-level primitive QCD amplitudes
- A differential operator for integrating one-loop scattering equations
- Fermions and the scattering equations
- CHY Theory for Several Fields