Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytic results for planar three-loop four-point integrals from a
  Knizhnik-Zamolodchikov equation   We apply a recently suggested new strategy to solve differential equations
for master integrals for families of Feynman integrals. After a set of master
integrals has been found using the integration-by-parts method, the crucial
point of this strategy is to introduce a new basis where all master integrals
are pure functions of uniform transcendentality. In this paper, we apply this
method to all planar three-loop four-point massless on-shell master integrals.
We explicitly find such a basis, and show that the differential equations are
of the Knizhnik-Zamolodchikov type. We explain how to solve the latter to all
orders in the dimensional regularization parameter epsilon, including all
boundary constants, in a purely algebraic way. The solution is expressed in
terms of harmonic polylogarithms. We explicitly write out the Laurent expansion
in epsilon for all master integrals up to weight six.

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The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
4
The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
1
The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg