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


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.

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Correspondence to Alexander Hock.

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ArXiv ePrint: 1908.04543

With an appendix by Robert Seiringer, Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria.

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Grosse, H., Hock, A. & Wulkenhaar, R. Solution of the self-dual Φ4 QFT-model on four-dimensional Moyal space. J. High Energ. Phys. 2020, 81 (2020).

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  • Integrable Field Theories
  • Matrix Models
  • Non-Commutative Geometry