acta physica slovaca |
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Acta Physica Slovaca 65, No.5, 369-468 (2015) (100 pages)
PHASE STRUCTURE OF FUZZY FIELD THEORIES AND MULTITRACE MATRIX MODELS Juraj Tekel Department of Theoretical Physics, Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia Full text: ::pdf :: (Received 30 October 2015, accepted 10 November 2015) Abstract: We review the interplay of fuzzy field theories and matrix models, with an emphasis on the phase structure of fuzzy scalar field theories. We give a self-contained introduction to these topics and give the details concerning the saddle point approach for the usual single trace and multitrace matrix models. We then review the attempts to explain the phase structure of the fuzzy field theory using a corresponding random matrix ensemble, showing the strength and weaknesses of this approach. We conclude with a list of challenges one needs to overcome and the most interesting open problems one can try to solve. PACS: 11.10.Nx, 11.10.Lm, 02.10.Yn Keywords: Multitrace matrix models, Noncommutative geometry, Fuzzy field theory, Phase diagram of fuzzy field theory |
ISSN 1336-040X (online) ISSN 0323-0465 (printed) For authors: ActaStyle.cls |
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