PIRSA:18120021 Scientific Series Quantum Fields and Strings

DOI10.48660/18120021

Series: Quantum Fields and Strings

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

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

@misc{ pirsa_PIRSA:18120021,
  doi = {10.48660/18120021},
  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.

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