One-cycle negative geometries in N=4 SYM have singularities only at z=-1, 0, and infinity to all loop orders.
Landau Singularities from the Amplituhedron
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abstract
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.
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hep-th 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Explicit three-loop computation of negative geometries for F(g,z) with all-loop resummation of one-cycle diagrams and extraction of the cusp anomalous dimension via z-integration.
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Landau Analysis of One-Cycle Negative Geometries
One-cycle negative geometries in N=4 SYM have singularities only at z=-1, 0, and infinity to all loop orders.
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Multi-Loop Negative Geometries
Explicit three-loop computation of negative geometries for F(g,z) with all-loop resummation of one-cycle diagrams and extraction of the cusp anomalous dimension via z-integration.