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arXiv · 1612.07584

The $\Phi^3_4$ and $\Phi^3_6$ matricial QFT models have reflection positive two-point function

Harald Grosse·Akifumi Sako·Raimar Wulkenhaar
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Abstract

We extend our previous work (on $D=2$) to give an exact solution of the $\Phi^3_D$ large-$\mathcal{N}$ matrix model (or renormalised Kontsevich model) in $D=4$ and $D=6$ dimensions. Induction proofs and the difficult combinatorics are unchanged compared with $D=2$, but the renormalisation - performed according to Zimmermann - is much more involved. As main result we prove that the Schwinger 2-point function resulting from the $\Phi^3_D$-QFT model on Moyal space satisfies, for real coupling constant, reflection positivity in $D=4$ and $D=6$ dimensions. The K\"all\'en-Lehmann mass spectrum of the associated Wightman 2-point function describes a scattering part $|p|^2 \geq 2\mu^2$ and an isolated fuzzy mass shell around $|p|^2=\mu^2$.

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Harald Grosse, Akifumi Sako, Raimar Wulkenhaar. 2016-12-22. The $\Phi^3_4$ and $\Phi^3_6$ matricial QFT models have reflection positive two-point function. https://arxiv.org/abs/1612.07584

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