The Φ43 and Φ63 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 ΦD3 large-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 ΦD3-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≥2μ2 and an isolated broadened mass shell around |p|2=μ2.