Christian Sämann, “The Multitrace Matrix Model of Scalar Field Theory on Fuzzy <nobr>$\mathbb CP^n$</nobr>”, SIGMA, 2010, Volume 6,050, 23 pp.

This article is cited in 23 papers

The Multitrace Matrix Model of Scalar Field Theory on Fuzzy $\mathbb CP^n$

Christian Sämann^ab

^a Maxwell Institute for Mathematical Sciences, Edinburgh, UK
^b Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS, UK

Abstract: We perform a high-temperature expansion of scalar quantum field theory on fuzzy $\mathbb CP^n$ to third order in the inverse temperature. Using group theoretical methods, we rewrite the result as a multitrace matrix model. The partition function of this matrix model is evaluated via the saddle point method and the phase diagram is analyzed for various $n$. Our results confirm the findings of a previous numerical study of this phase diagram for $\mathbb CP^1$.

Keywords: matrix models; fuzzy geometry.

MSC: 81T75

Received: March 25, 2010; in final form June 3, 2010; Published online June 11, 2010

Language: English

DOI: 10.3842/SIGMA.2010.050