4 research outputs found
Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops
In this sequel to arXiv:1711.11507 we classify the boundaries of amplituhedra
relevant for determining the branch points of general two-loop amplitudes in
planar super-Yang-Mills theory. We explain the connection to
on-shell diagrams, which serves as a useful cross-check. We determine the
branch points of all two-loop NMHV amplitudes by solving the Landau equations
for the relevant configurations and are led thereby to a conjecture for the
symbol alphabets of all such amplitudes.Comment: 42 pages, 6 figures, 8 tables; v2: minor corrections and improvement
Landau Singularities from the Amplituhedron
We propose a simple geometric algorithm for determining the complete set of
branch points of amplitudes in planar N=4 super-Yang-Mills theory directly from
the amplituhedron, without resorting to any particular representation in terms
of local Feynman integrals. This represents a step towards translating
integrands directly into integrals. In particular, the algorithm provides
information about the symbol alphabets of general amplitudes. We illustrate the
algorithm applied to the one- and two-loop MHV amplitudes.Comment: 34 pages, 16 figures; v2: minor corrections and improvement
All-Helicity Symbol Alphabets from Unwound Amplituhedra
We review an algorithm for determining the branch points of general
amplitudes in planar super-Yang-Mills theory from amplituhedra.
We demonstrate how to use the recent reformulation of amplituhedra in terms of
`sign flips' in order to streamline the application of this algorithm to
amplitudes of any helicity. In this way we recover the known branch points of
all one-loop amplitudes, and we find an `emergent positivity' on boundaries of
amplituhedra.Comment: 38 pages, 5 figures, 1 big table; v2: minor corrections and
improvement