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 SIGMA, 2010, Volume 6, 050, 23 pages (Mi sigma507)

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

Christian Sämannab

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

DOI: https://doi.org/10.3842/SIGMA.2010.050

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ArXiv: 1003.4683
MSC: 81T75
Received: March 25, 2010; in final form June 3, 2010; Published online June 11, 2010
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Citation: Christian Sämann, “The Multitrace Matrix Model of Scalar Field Theory on Fuzzy $\mathbb CP^n$”, SIGMA, 6 (2010), 050, 23 pp.

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\Bibitem{Sam10} \by Christian S\"amann \paper The Multitrace Matrix Model of Scalar Field Theory on Fuzzy $\mathbb CP^n$ \jour SIGMA \yr 2010 \vol 6 \papernumber 050 \totalpages 23 \mathnet{http://mi.mathnet.ru/sigma507} \crossref{https://doi.org/10.3842/SIGMA.2010.050} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2725033} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000279673500003} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84896064036} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Ihl M., Sachse Ch., Saemann Ch., “Fuzzy scalar field theory as matrix quantum mechanics”, Journal of High Energy Physics, 2011, no. 3, 091
2. Ydri B., Bouchareb A., “The Fate of the Wilson-Fisher Fixed Point in Non-Commutative Phi(4)”, J. Math. Phys., 53:10 (2012), 102301
3. Tekel J., “Random Matrix Approach to Scalar Fields on Fuzzy Spaces”, Phys. Rev. D, 87:8 (2013), 085015
4. Polychronakos, AP, “Effective action and phase transitions of scalar field on the fuzzy sphere”, Physical Review D, 88:6 (2013), 065010
5. Tekel J., “Uniform Order Phase and Phase Diagram of Scalar Field Theory on Fuzzy Cpn”, J. High Energy Phys., 2014, no. 10, 144
6. Ydri B., “New Algorithm and Phase Diagram of Noncommutative (4) on the Fuzzy Sphere”, J. High Energy Phys., 2014, no. 3, 065
7. Saemann Ch., “Bootstrapping Fuzzy Scalar Field Theory”, J. High Energy Phys., 2015, no. 4, 044
8. Tekel J., “Matrix Model Approximations of Fuzzy Scalar Field Theories and Their Phase Diagram”, J. High Energy Phys., 2015, no. 12, 176
9. Ydri B., Ahmim R., Bouchareb A., “Wilson Rg of Noncommutative Phi(4)(4)”, Int. J. Mod. Phys. A, 30:33 (2015), 1550195
10. Rea S., Saemann Ch., “the Phase Diagram of Scalar Field Theory on the Fuzzy Disc”, J. High Energy Phys., 2015, no. 11, 115
11. Tekel J., “Phase Structure of Fuzzy Field Theories and Multitrace Matrix Models”, Acta Phys. Slovaca, 65:5 (2015), 369–469
12. Ydri B., Ramda K., Rouag A., Phys. Rev. D, 93:6 (2016), 065056
13. Ydri B., Rouag A., Ramda K., “Emergent geometry from random multitrace matrix models”, Phys. Rev. D, 93:6 (2016), 065055
14. Ydri B., Phys. Rev. D, 93:6 (2016), 065041
15. Ydri B., Soudani Ch., Rouag A., “Quantum Gravity as a Multitrace Matrix Model”, Int. J. Mod. Phys. A, 32:31 (2017), 1750180
16. Ydri B., “Introductory Remarks”: Ydri, B, Lectures on Matrix Field Theory, Lecture Notes in Physics, 929, Springer International Publishing Ag, 2017, 1–18
17. Ydri B., “Quantum Noncommutative Phi-Four”: Ydri, B, Lectures on Matrix Field Theory, Lecture Notes in Physics, 929, Springer International Publishing Ag, 2017, 119–206
18. Ydri B., “The Multitrace Approach”: Ydri, B, Lectures on Matrix Field Theory, Lecture Notes in Physics, 929, Springer International Publishing Ag, 2017, 207–275
19. Tekel J., “Asymmetric Hermitian Matrix Models and Fuzzy Field Theory”, Phys. Rev. D, 97:12 (2018), 125018
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