A Laplacian to Compute Intersection Numbers on M¯_g,nand Correlation Functions in NCQFT

Autor(en)

Alexander Hock, Harald Grosse, Raimar Wulkenhaar

Abstrakt

Let Fg(t) be the generating function of intersection numbers of ψ-classes on the moduli spaces (Formula presented.) of stable complex curves of genus g. As by-product of a complete solution of all non-planar correlation functions of the renormalised Φ 3-matrical QFT model, we explicitly construct a Laplacian Δ t on a space of formal parameters ti which satisfies exp (∑ g≥2N2-2gFg(t)) = exp ((- Δ t+ F2(t)) / N2) 1 as formal power series in 1 / N2. The result is achieved via Dyson-Schwinger equations from noncommutative quantum field theory combined with residue techniques from topological recursion. The genus-g correlation functions of the Φ 3-matricial QFT model are obtained by repeated application of another differential operator to Fg(t) and taking for ti the renormalised moments of a measure constructed from the covariance of the model.

Organisation(en)

Mathematische Physik

Externe Organisation(en)

University of Oxford, Universität Münster

Journal

Communications in Mathematical Physics

Band

399

Seiten

481–517

Anzahl der Seiten

37

ISSN

0010-3616

DOI

https://doi.org/10.1007/s00220-022-04557-w

Publikationsdatum

01-2023

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

ASJC Scopus Sachgebiete

Statistical and Nonlinear Physics, Mathematical Physics

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/9975746d-e667-4b2a-bdcc-813733c33a5e