PIRSA:18120021

A Bestiary of Feynman Integral Calabi-Yaus

APA

von Hippel, M. (2018). A Bestiary of Feynman Integral Calabi-Yaus. Perimeter Institute. https://pirsa.org/18120021

MLA

von Hippel, Matt. A Bestiary of Feynman Integral Calabi-Yaus. Perimeter Institute, Dec. 11, 2018, https://pirsa.org/18120021

BibTex

          @misc{ pirsa_18120021,
            doi = {},
            url = {https://pirsa.org/18120021},
            author = {von Hippel, Matt},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {A Bestiary of Feynman Integral Calabi-Yaus},
            publisher = {Perimeter Institute},
            year = {2018},
            month = {dec},
            note = {PIRSA:18120021 see, \url{https://pirsa.org}}
          }
          

Abstract

While the simplest Feynman diagrams evaluate to multiple polylogarithms, more complicated functions can arise, involving integrals over higher-dimensional manifolds. Surprisingly, all examples of such manifolds in the literature to date are Calabi-Yau. I discuss why this is, and prove that a specific class of "marginal" diagrams give rise to Calabi-Yau manifolds. I demonstrate a bound on the dimensionality of these manifolds with loop order, and present infinite families of diagrams that saturate this bound to all orders.