Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Biadjoint scalar tree amplitudes and intersecting dual associahedra   We present a new formula for the biadjoint scalar tree amplitudes
$m(\alpha|\beta)$ based on the combinatorics of dual associahedra. Our
construction makes essential use of the cones in 'kinematic space' introduced
by Arkani-Hamed, Bai, He, and Yan. We then consider dual associahedra in 'dual
kinematic space.' If appropriately embedded, the intersections of these dual
associahedra encode the amplitudes $m(\alpha|\beta)$. In fact, we encode all
the partial amplitudes at $n$-points using a single object (a fan) in dual
kinematic space. Equivalently, as a pleasant corollary of our construction, all
$n$-point partial amplitudes can be understood as coming from integrals over
subvarieties in a single toric variety. Explicit formulas for the amplitudes
then follow by evaluating these integrals using the equivariant localisation
(or Duistermaat-Heckman) formula. Finally, by introducing a lattice in
kinematic space, we observe that our fan is also related to the inverse KLT
kernel, sometimes denoted $m_{\alpha'}(\alpha|\beta)$.

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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: math
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph