Chern-Simons-Witten Theory as a Topological Fermi Liquid

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 YM2 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 YM2, 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.