Chern-Simons-Witten Theory as a Topological Fermi Liquid

Abstract

We reinterpret U(N) Chern-Simons-Witten theory quantized on a torus as a free fermion system. Its Hilbert space and some observables are simply related to those of group quantum mechanics, even at finite N and k. Its large N limit can be described using techniques developed for matrix quantum mechanics and two-dimensional Yang-Mills theory. We discuss the bosonization of this theory, which for YM_2 gave a precise interpretation of Wilson loop operators in terms of string creation and annihilation operators, and examine its consequences for a string interpretation here. The formalism seems entirely adequate for the leading large N results and in a sense can be thought of as a `classical string field theory'. In considering subleading orders in 1/N, we identify some major differences between CSW and YM_2, which must be dealt with to find a CSW gauge string interpretation. Although these particular differences are probably not relevant for `QCD string,' they do illustrate some of the issues there, and we comment on this. We also propose an approach to dealing with large N transitions.

RU-94-29, 30 pp, 1 figure, harvmac

References in corpus (3)

• The Verlinde Algebra And The Cohomology Of The Grassmannian
• Large N 2D Yang-Mills Theory and Topological String Theory
• Semiclassical Tunneling in 1+1 Dimensional String Theory

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• Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory
• Discrete and oscillatory Matrix Models in Chern-Simons theory
• Comments on Half S-Branes
• Topological Gravity as Large N Topological Gauge Theory
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• Domain Walls in 4d N=1 Supersymmetric Yang-Mills
• Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons Theory on Torus Bundles
• Geometric Transitions, del Pezzo Surfaces and Open String Instantons
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