Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday

Collection Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday

Organizer(s) Erik PANZER (University of Oxford) & Karen YEATS (University of Waterloo)
Date(s) 16/11/2020 - 20/11/2020
linked URL https://indico.math.cnrs.fr/event/4834/
00:00:00 / 00:00:00
19 28

Solution of $\phi^4_4$ on the Moyal Space

By Alexander Hock

We show the exact solution of the self-dual $\phi^4_4$-model on the 4-dimensional Moyal space. Using the results explained in Raimar's talk, an implicitly defined function converges to a Fredholm integral, which is solved, for any coupling constant $\lambda>-\frac{1}{\pi}$, in terms of a hypergeometric function. We prove that the interacting model has spectral dimension $4-2\frac{\arcsin(\lambda\pi)}{\pi}$ for $|\lambda|<\frac{1}{\pi}$. It is this dimension drop which for $\lambda>0$ avoids the triviality problem of the $\phi^4_4$ model on the Moyal space.

Information about the video

  • Date of recording 19/11/2020
  • Date of publication 30/11/2020
  • Institution IHES
  • Language English
  • Audience Researchers
  • Format MP4

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