Solution of the self-dual Φ4 QFT-model on four-dimensional Moyal space

  • Harald Grosse
  • Alexander HockEmail author
  • Raimar Wulkenhaar
Open Access
Regular Article - Theoretical Physics


Previously the exact solution of the planar sector of the self-dual Φ4-model on 4-dimensional Moyal space was established up to the solution of a Fredholm integral equation. This paper solves, for any coupling constant λ > −\( \frac{1}{\uppi} \), the Fredholm equation in terms of a hypergeometric function and thus completes the construction of the planar sector of the model. We prove that the interacting model has spectral dimension 4 2 \( \frac{\arcsin \left(\uplambda \uppi \right)}{\uppi} \) for |λ| <\( \frac{1}{\uppi} \). It is this dimension drop which for λ > 0 avoids the triviality problem of the matricial \( {\varPhi}_4^4 \)-model. We also establish the power series approximation of the Fredholm solution to all orders in λ. The appearing functions are hyperlogarithms defined by iterated integrals, here of alternating letters 0 and 1. We identify the renormalisation parameter which gives the same normalisation as the ribbon graph expansion.


Integrable Field Theories Matrix Models Non-Commutative Geometry 


Open Access

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© The Author(s) 2020

Authors and Affiliations

  1. 1.Fakultät für PhysikUniversität WienViennaAustria
  2. 2.Mathematisches Institut der Westfälischen Wilhelms-UniversitätMünsterGermany
  3. 3.Erwin Schrödinger International Institute for Mathematics and PhysicsUniversity of ViennaViennaAustria

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