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

This article is cited in 19 scientific papers (total in 19 papers)

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

Full text: PDF file (375 kB)
Full text: http://emis.mi.ras.ru/journals/SIGMA/2010/050/
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Bibliographic databases:

ArXiv: 1003.4683
MSC: 81T75
Received: March 25, 2010; in final form June 3, 2010; Published online June 11, 2010
Language:

Citation: Christian Sämann, “The Multitrace Matrix Model of Scalar Field Theory on Fuzzy $\mathbb CP^n$”, SIGMA, 6 (2010), 050, 23 pp.

Citation in format AMSBIB
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\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
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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  crossref  mathscinet  zmath  isi  scopus
    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  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Tekel J., “Random Matrix Approach to Scalar Fields on Fuzzy Spaces”, Phys. Rev. D, 87:8 (2013), 085015  crossref  adsnasa  isi  elib  scopus
    4. Polychronakos, AP, “Effective action and phase transitions of scalar field on the fuzzy sphere”, Physical Review D, 88:6 (2013), 065010  crossref  adsnasa  isi  elib  scopus
    5. Tekel J., “Uniform Order Phase and Phase Diagram of Scalar Field Theory on Fuzzy Cpn”, J. High Energy Phys., 2014, no. 10, 144  crossref  isi  elib  scopus
    6. Ydri B., “New Algorithm and Phase Diagram of Noncommutative (4) on the Fuzzy Sphere”, J. High Energy Phys., 2014, no. 3, 065  crossref  mathscinet  isi  scopus
    7. Saemann Ch., “Bootstrapping Fuzzy Scalar Field Theory”, J. High Energy Phys., 2015, no. 4, 044  crossref  isi  scopus
    8. Tekel J., “Matrix Model Approximations of Fuzzy Scalar Field Theories and Their Phase Diagram”, J. High Energy Phys., 2015, no. 12, 176  crossref  mathscinet  zmath  isi  elib  scopus
    9. Ydri B., Ahmim R., Bouchareb A., “Wilson Rg of Noncommutative Phi(4)(4)”, Int. J. Mod. Phys. A, 30:33 (2015), 1550195  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    10. Rea S., Saemann Ch., “the Phase Diagram of Scalar Field Theory on the Fuzzy Disc”, J. High Energy Phys., 2015, no. 11, 115  crossref  mathscinet  zmath  isi  elib  scopus
    11. Tekel J., “Phase Structure of Fuzzy Field Theories and Multitrace Matrix Models”, Acta Phys. Slovaca, 65:5 (2015), 369–469  isi  elib
    12. Ydri B., Ramda K., Rouag A., Phys. Rev. D, 93:6 (2016), 065056  crossref  mathscinet  isi  scopus
    13. Ydri B., Rouag A., Ramda K., “Emergent geometry from random multitrace matrix models”, Phys. Rev. D, 93:6 (2016), 065055  crossref  mathscinet  isi  scopus
    14. Ydri B., Phys. Rev. D, 93:6 (2016), 065041  crossref  mathscinet  isi  scopus
    15. Ydri B., Soudani Ch., Rouag A., “Quantum Gravity as a Multitrace Matrix Model”, Int. J. Mod. Phys. A, 32:31 (2017), 1750180  crossref  mathscinet  zmath  isi  scopus
    16. Ydri B., “Introductory Remarks”: Ydri, B, Lectures on Matrix Field Theory, Lecture Notes in Physics, 929, Springer International Publishing Ag, 2017, 1–18  crossref  mathscinet  isi  scopus
    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  crossref  mathscinet  isi  scopus
    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  crossref  mathscinet  isi  scopus
    19. Tekel J., “Asymmetric Hermitian Matrix Models and Fuzzy Field Theory”, Phys. Rev. D, 97:12 (2018), 125018  crossref  mathscinet  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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