2021/05/02 by Susama Agarwala, Agarwala, Susama, Cameron Marcott +1
Agricultural and Biological Sciences · Engineering · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Muon and positron interactions and applications #Plant nutrient uptake and metabolism
paper · pdf · doi:10.48550/arxiv.2105.00541
openalex publication_date 2021/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper shows that not only do the codimension one spurious poles of Nk MHV tree level diagrams in N=4 SYM theory cancel in the tree level amplitude as expected, but their vanishing loci have a geometric interpretation that is tightly connected to their representation in the positive Grassmannians. In general, given a positroid variety, Σ, and a minimal matrix representation of it in terms of independent variable valued matrices, MV, one can define a polynomial, R(V) that is uniquely defined by the Grassmann necklace, I, of the positroid cell. The vanishing locus of R(V) lies on the boundary of the positive variety Σ ∖ Σ, but not all boundaries intersect the vanishing loci of a factor of R(V). We use this to show that the codimension one spurious poles of N=4 SYM, represented in twistor space, cancel in the tree level amplitude.