Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scattering Forms, Worldsheet Forms and Amplitudes from Subspaces   We present a general construction of two types of differential forms, based
on any $(n{-}3)$-dimensional subspace in the kinematic space of $n$ massless
particles. The first type is the so-called projective, scattering forms in
kinematic space, while the second is defined in the moduli space of
$n$-punctured Riemann spheres which we call worldsheet forms. We show that the
pushforward of worldsheet forms, by summing over solutions of scattering
equations, gives the corresponding scattering forms, which generalizes the
results of [1711.09102]. The pullback of scattering forms to subspaces can have
natural interpretations as amplitudes in terms of Bern-Carrasco-Johansson
double-copy construction or Cachazo-He-Yuan formula. As an application of our
formalism, we construct in this way a large class of $d\log$ scattering forms
and worldsheet forms, which are in one-to-one correspondence with non-planar
MHV leading singularities in ${\cal N}=4$ super-Yang-Mills. For every leading
singularity function, we present a new determinant formula in moduli space, as
well as a (combinatoric) polytope and associated scattering form in kinematic
space. These include the so-called Cayley cases, where in each case the
scattering form is the canonical forms of a convex polytope in the subspace,
and scattering equations admit elegant rewritings as a map from the moduli
space to the subspace.

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The categories of this paper are: solv-int
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn