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

Autor(en)

Harald Grosse, Akifumi Sako, Raimar Wulkenhaar

Abstrakt

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

Organisation(en)

Mathematische Physik

Externe Organisation(en)

Universität Münster, Tokyo University of Science

Journal

Nuclear Physics, Section B

Band

926

Seiten

20-48

Anzahl der Seiten

29

ISSN

0550-3213

DOI

https://doi.org/10.1016/j.nuclphysb.2017.10.022

Publikationsdatum

12-2016

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

Schlagwörter

ASJC Scopus Sachgebiete

Nuclear and High Energy Physics

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/b3233c8a-e758-44f0-a045-60c2d1e88435