Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 050, 23 pages      arXiv:1003.4683      https://doi.org/10.3842/SIGMA.2010.050
Contribution to the Special Issue “Noncommutative Spaces and Fields”

The Multitrace Matrix Model of Scalar Field Theory on Fuzzy CPn

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

Received March 25, 2010, in final form June 03, 2010; Published online June 11, 2010

Abstract
We perform a high-temperature expansion of scalar quantum field theory on fuzzy CPn 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 CP1.

Key words: matrix models; fuzzy geometry.

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