Large N field theories II

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Winter '08

General references for the first half of this quarter are Peskin & Schroeder, and Coleman's Aspects of Symmetry chapter 8. If you don't have Coleman's book, you can download his 1/N lecture notes here.

1/18 - Nonlinear sigma model with O(N) symmetry
  • Chris Vermilion
  • Abstract - I will begin with an overview of the quarter's talks. My talk will begin with a discussion of a simple O(N) vector model and its large-N limit. I will show how this model is related to the linear and non-linear sigma models, then discuss the NLSM at length. I will show that the NLSM can be solved exactly in the large-N limit, with some specific comments for the case d=2.
  • Refs -
    • Coleman, Aspects of Symmetry, chapter on 1/N expansion
    • Peskin and Schroeder, 13.3.
1/25 - Gross-Neveu model
  • Rob Schabinger
  • Abstract - This week I'll be talking about the Gross-Neveu model. This model will illustrate that we can see many of the interesting features (at large N) that we saw last week in the non-linear sigma model in a theory where we have a chiral condensate instead of a elementary scalar acquiring a vacuum expectation value.
  • Refs -
    • Gross and Neveu, "Dynamical Symmetry Breaking in Asymptotically Free Field Theories", Phys. Rev. D10, 3235 (1974)
2/1 - Dominance of planar diagrams
  • Amy Nicholson
  • Abstract - I'll be talking about the dominance of planar diagrams for U(N) gauge theories at large N. I'll then discuss some general phenomenology which results, and finally I'll briefly discuss the relation to dual string models.
  • Refs -
    • 't Hooft, "A Planar Diagram Theory for Strong Interactions", Nucl. Phys. B72, 461, (1974)
    • Manohar, "Large N QCD", hep-ph/9802419
    • First chapters of AdS/CFT references from last quarter:
2/8 - 't Hooft model, a.k.a. QCD_2
  • Jon Walsh
  • Abstract - QCD in 2d at large N.
  • Refs -
    • 't Hooft, Nucl. Phys. B75, 461 (1974)
    • Coleman, Aspects of Symmetry, sec. 3.3
    • Manohar, hep-ph/9802419
2/15 - Gross-Witten model
  • Kristan Jensen
  • Abstract - Today we will examine the gross-witten model: pure U(N) yang-mills on a (1+1)-dimensional lattice at N=infinity. we will analytically compute the 'free energy' of the theory - where we regard the 't Hooft coupling as the 'temperature' - and show that it exhibits a third-order phase transition.
  • Refs -
    • Gross and Witten, Phys. Rev. D21, 446 (1980)
2/22 - Baryons in the 1/N expansion I
  • Ethan Thompson
  • Abstract - I'll be talking about phenomenology at large N - despite the title on the webpage, a good deal of my talk will be about mesons, with some baryon material at the end.
  • Refs -
    • Coleman's large N lecture
    • Manohar's review hep-ph/9802419
    • Witten, Nucl. Phys. B160, 57-115 (1979)
    • Coleman and Witten, PRL 45, 100
2/29 - Baryons in the 1/N expansion II
  • Andrew Lytle
  • Abstract - Today we will discuss baryons at large N. I will demonstrate the spin-flavor symmetry of the baryon spectrum at large N, and calculate axial vector matrix elements, with 1/N corrections time permitting.
  • Refs -
    • Dashen, Jenkins, and Manohar, Phys. Rev. D49, 4713 (1994)
    • Manohar's "Large N QCD" review hep-th/9802419.
3/14 - Large N limits as classical mechanics
  • Steve Paik
  • Abstract - We will show how to find classical limits of quantum theories that obey certain conditions. Notions of classical operators, Poisson brackets and phase space will be introduced. We will use ordinary quantum mechanics in one dimension to illustrate these abstract concepts.
  • Refs -
    • L. Yaffe, Rev. Mod. Phys. 54, 407 (1982)
3/21 - Eguchi-Kawai reduction
  • Jong-Wan Lee
  • Abstract - The pure U(N) lattice gauge theory in d-dimension can be reduced to the single plaquette model in the large-N limit. I will show this equivalence using the loop equations, Schwinger-Dyson equations, and the factorization property of large N gauge theory.
  • Refs -
    • Eguchi and Kawai, "Reduction of Dynamical Degrees of Freedom in the Large-N Gauge Theory", PRL 48, 1063 (1982).
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