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

TL;DR

This paper provides an exact solution for certain large-N matrix quantum field theory models in four and six dimensions, demonstrating reflection positivity of the two-point function and analyzing the mass spectrum.

Contribution

It extends previous work to higher dimensions, proving reflection positivity and analyzing the mass spectrum for the $\

Findings

Reflection positivity of the two-point function in D=4 and D=6.

Exact solution of the $\

paper_type":"empirical"}}# Answer {

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 $|p|^2=\mu^2$.