Chiral condensate, master field, constituent quark and all that in QCD in two-dimensions (N ---> infinity)
Jan, 199518 pages
Published in:
- Phys.Lett.B 362 (1995) 105-112
e-Print:
- hep-ph/9502258 [hep-ph]
Report number:
- SMU-HEP-94-10
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Abstract:
We discuss the various aspects of two-dimensional (the 't Hooft model\cite{Hooft}). Our main interest (motivated by the corresponding analysis in the four dimensional QCD) is the vacuum structure of the theory. We use the very general methods in the analysis, such as dispersion relations and duality in order to relate the known spectrum of to the different vacuum characteristics. We explicitly calculate (in terms of physical parameters like masses and matrix elements) the chiral condensate as well as the mixed vacuum condensates: \la 0|\bar{q}(g\epsilon_{\mu\nu} G_{\mu\nu})~nq |0\ra \sim M_{eff}~{2n}\la 0|\bar{q} q |0\ra . The vacuum expectation value of the nonlocal, string operator (Wilson line): \la 0| W |0\ra \equiv \la 0|\bar{q}(x) e~{ig\int_0~xA_{\mu}dx_{\mu}}q(0) |0\ra \sim J_0(M_{eff}\cdot x) is also obtained. Such an object naturally arises in the description of the heavy-light quark system. We interpret the factorization property for the mixed vacuum condensates shown above as a reminiscent of the master field at large . Bearing in mind that the gauge-variant function \la 0| \bar{q}(x) q(0)|0 \ra describes the propagator of the original quark field, we interpret the similar, but gauge invariant object \la 0| W|0 \ra which is turned out to be Bessel function, as a two-dimensional free propagator of the effective constituent quark with imaginary mass.Note:
- 18 pages, Report-no: SMU-HEP-94-10
- gauge field theory: SU(N)
- fermion: condensation
- dimension: 2
- expansion 1/N
- Wilson loop
- phase space
- bibliography
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