Strong-coupling planar diagrams,random surfaces,and the large-N phase transition in U(N) lattice gauge theories |
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| Institution: | 2. Department of Obstetrics and Gynecology, Wayne State University School of Medicine, Detroit, MI;3. Department of Obstetrics and Gynecology, University of Michigan, Ann Arbor, MI;4. Department of Epidemiology and Biostatistics, Michigan State University, East Lansing, MI;5. Center for Molecular Medicine and Genetics, Wayne State University, Detroit, MI;6. Detroit Medical Center, Detroit, MI;7. Department of Obstetrics and Gynecology, Florida International University, Miami, FL;8. Department of Obstetrics and Gynecology, Hadassah-Hebrew University Medical Center, Jerusalem, Israel;9. Maternity Department “D,” Division of Obstetrics and Gynecology, Soroka University Medical Center, School of Medicine, Beer-Sheva, Israel;10. Faculty of Health Sciences, Ben Gurion University of the Negev, Beer-Sheva, Israel;11. Center for Research and Innovation in Maternal-Fetal Medicine, Department of Obstetrics and Gynecology, Sótero del Río Hospital, Santiago, Chile;12. Division of Obstetrics and Gynecology, Faculty of Medicine, Pontificia Universidad Católica de Chile, Santiago, Chile;13. Office of Women’s Health, Integrative Biosciences Center, Wayne State University, Detroit, MI;14. Department of Physiology, Wayne State University School of Medicine, Detroit, MI;15. Department of Computer Science, Wayne State University College of Engineering, Detroit, MI;1. Physikalisch-Technische Bundesanstalt, Brunswick and Berlin, Germany;2. Freie Universität Berlin, Germany;1. Maternal-Fetal Medicine Division, Department of Obstetrics and Gynecology, University of Illinois at Chicago, Chicago, IL;2. College of Medicine, University of Illinois at Chicago, Chicago, IL;3. Maternal-Fetal Medicine Catholic Health System Long Island, New York, NY;4. Department of Obstetrics and Gynecology, John Hopkins University, 600 North Wolfe Street, Baltimore, MD;1. Institute of Mathematics, Technical University Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany;2. Fakultät für Mathematik, University of Bielefeld, Postfach 100131, 33501 Bielefeld, Germany;1. Graduate student, Assistant Professor of Department of Operative Dentistry, University School of Dental Medicine, University of Oviedo, Asturias, Spain;2. Associate Professor, Department of Operative Dentistry, University School of Dental Medicine, University of Oviedo, Asturias, Spain;3. Professor, Department of Oral and Maxillofacial Surgery and Oral Medicine, University School of Dental Medicine, University of Oviedo, Asturias, Spain;4. Professor, Department of Oral and Maxillofacial Surgery and Oral Medicine, University School of Dental Medicine, University of Oviedo, Asturias, Spain |
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| Abstract: | The strong-coupling expansion of U(N) gauge theory on a D-dimensional lattice is reformulated in the limit N → ∞ through a set of diagrammatic rules directly for the free energy and Wilson loops. The strong-coupling planar diagrams are interpreted as surfaces embedded in the lattice. The large-N phase transition is related to the entropy of these surfaces. It is shown that the strong-coupling phase of the U(∞) gauge theory terminates with a phase transition of Gross-Witten type only in 2 and 3 dimensions. When D⩾4 the large-N singularity takes place in a metastable phase because of an earlier first-order transition to the weak-coupling phase of the theory. |
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