2024/01/10 by Susama Agarwala, Colleen Delaney, Agarwala, Susama +3
Engineering · Mathematics · Physics and Astronomy · #81T60 #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Mathematical Physics (math-ph) #Muon and positron interactions and applications #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2401.05592
openalex publication_date 2024/01/10 · openalex created_date 2024/01/13 · openalex updated_date 2026/08/01
We study the boundaries of the positroid cells which arise from N = 4 super Yang Mills theory. Our main tool is a new diagrammatic object which generalizes the Wilson loop diagrams used to represent interactions in the theory. We prove conditions under which these new generalized Wilson loop diagrams correspond to positroids and give an explicit algorithm to calculate the Grassmann necklace of said positroids. Then we develop a graphical calculus operating directly on noncrossing generalized Wilson loop diagrams. In this paradigm, applying diagrammatic moves to a generalized Wilson loop diagram results in new diagrams that represent boundaries of its associated positroid, without passing through cryptomorphisms. We provide a Python implementation of the graphical calculus and use it to show that the boundaries of positroids associated to ordinary Wilson loop diagram are generated by our diagrammatic moves in certain cases.