Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Comments on all-loop constraints for scattering amplitudes and Feynman
  integrals   We comment on the status of "Steinmann-like" constraints, i.e. all-loop
constraints on consecutive entries of the symbol of scattering amplitudes and
Feynman integrals in planar ${\cal N}=4$ super-Yang-Mills, which have been
crucial for the recent progress of the bootstrap program. Based on physical
discontinuities and Steinmann relations, we first summarize all possible double
discontinuities (or first-two-entries) for (the symbol of) amplitudes and
integrals in terms of dilogarithms, generalizing well-known results for $n=6,7$
to all multiplicities. As our main result, we find that extended-Steinmann
relations hold for all finite integrals that we have checked, including various
ladder integrals, generic double-pentagon integrals, as well as finite
components of two-loop NMHV amplitudes for any $n$; with suitable normalization
such as minimal subtraction, they hold for $n=8$ MHV amplitudes at three loops.
We find interesting cancellation between contributions from rational and
algebraic letters, and for the former we have also tested cluster-adjacency
conditions using the so-called Sklyanin brackets. Finally, we propose a list of
possible last-two-entries for $n$-point MHV amplitudes derived from $\bar{Q}$
equations, which can be used to reduce the space of functions for higher-point
MHV amplitudes.

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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: nucl-th