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16:750:693 Applications of large N - spring 2008 H. Neuberger Classes shall meet Tuesdays and Fridays in ARC 108, 12:00-1:20 PM Textbook: Methods of Contemporary Gauge Theory, Yuri Makeenko, Cambridge University Press, (2002) Mane of the lectures will be based on original articles, rather than on the textbook. of the classes within the semester, before the reading period. Every student will need to make at least one such presentation. Participation in class is important and you need to attend most classes. My office hour is: Fridays, 2:30-3:30 in my office. My telephone number is 5-2284 and my electronic mail address is here. For any issue you wish to take up with me that does not require a real conversation (including setting up an appointment to meet if the office hour is inconvenient) email is the most efficient way to get a quick response. After the add/drop period attendance will be restricted to registered students. RUNNING PROGRESS REPORT Jan. 22: Lecture 1, Linear sigma model, based on t Hooft, hep-th/0204069; Coleman, Jackiw, Politzer, PRD10 (1974) 2491. Jan. 25: Lecture 2, Gross-Neveu model, based on Coleman, 1/N, March 1980, SLAC_PUB-2484. Jan. 29: Lecture 3, Jan. 31: Lecture 4, Feb. 5: Lecture 5, The CP(N-1) model and related issues: based on Coleman, 1/N, March 1980, SLAC_PUB-2484; Witten, NPB149 (1979) 285; Perelomov, Phys. Rep. 146(1987) 135; Witten, NPB145(1978) 110; Coleman, Jackiw, Politzer, PRD10 (1974) 2491 Feb. 8: Lecture 6, The supersymmetric CP(N-1) model, Student lecture, based on Witten, NPB149 (1979) 285. Feb. 13: Lecture 7, Chiral Gross-Neveu model; double line propagators, based on Witten, NPB149 (1979) 285 and on t Hooft, hep-th/0204069 and on Coleman, 1/N, March 1980, SLAC_PUB-2484. Feb. 15: Lecture 8, Large N QCD, based on Coleman, 1/N, March 1980, SLAC_PUB-2484, and Witten NPB 160(1977) 57. Feb. 19: Lecture 9, Mesons at large N, based on Coleman, 1/N, March 1980, SLAC_PUB-2484, and Witten NPB 160(1977) 57. Feb. 22: Classes canceled university wide (lost one lecture). Feb. 26: Lecture 10, Large N counting rules using sources; two dimensional QCD, based on folklore and Coleman, 1/N, March 1980, SLAC_PUB-2484, t Hooft, NPB75 (1974) 461. Feb. 26: Lecture 11, Large N and Quantum Mechanics, Student Lecture, based on Mlodinow and Papanicolaou, Ann. Phys. 128(1980) 314. March 4: Lecture 12, Quark propagator in two dimensional QCD; the Bethe-Salpeter equation, based on Field Theory textbooks by Sterman and by Itzykson&Zuber. March 7: Lecture 13, Meson states in two dimensional QCD, in addition to papers used in Lecture 10, based on the appendix of Kiskis et. al., Phys. Rev. D66 (2002) 025019. March 11: Lecture 14, The pion in planar 2D QCD and the asymptotic behavior of the meson spectrum, in addition to papers used in Lecture 13, R. Narayanan et. al., PLB 616 (2005) 76. March 14: Lecture 15, LGT, Textbook, Chapter 6.1 6.3. March 18, 21: Spring Break. March 25: Lecture 16, LGT and strong coupling expansion, Textbook : Chapter 6.4 March 28: Lecture 17, Baryons at large N -- I Student lecture. April 1: Lecture 18, Lattice Loop Equation, Textbook, Problem 12.6 April 4: Lecture 19, Baryons at large N -- II Student lecture. April 8: Lecture 20, Planar diagram counting: Tutte, CAN. J. MATH. 14(1962) 21; Koplik, Neveu, Nussinov, NPB123 (1977) 109. April 11: Lecture 21, Theta angle at large N Student lecture. April 15: Lecture 22, Matrix model counting, large N criticality, Brezin, Itzykson, Parisi, Zuber, Comm. Math. Phys. 59 (1978) 35, H. N., NPB 352 (1991) 689. April 18: Lecture 23, Nonequilibrium at large N in vector theories Student lecture. April 22: Lecture 24, Large N criticality, Loop equations on the lattice. April 25: Lecture 25, Large N reduction. April 29: Lecture 26, Loop equations and large N reduction in continuum. Makeup Lecture: (April 25, 2:30 3: 50 PM): Lecture 27, More about Baryons. Special Announcements (check often) Herbert Neuberger 2008-02-18 |