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

Abstract

We extend our previous work (on $D=2$) to give an exact solution of the $Φ^3_D$ 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 $Φ^3_D$-QFT model on Moyal space satisfies, for real coupling constant, reflection positivity in $D=4$ and $D=6$ dimensions. The Källén-Lehmann mass spectrum of the associated Wightman 2-point function describes a scattering part $|p|^2 \geq 2μ^2$ and an isolated fuzzy mass shell around $|p|^2=μ^2$.

31 pages, 2 figures. LaTeX. Dedicated to the memory of Wolfhart Zimmermann. v2: update of arXiv:1610.00526 permitted to suppress 3 pages