Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-10-26
Nucl.Phys.B468:383-419,1996
Physics
High Energy Physics
High Energy Physics - Theory
40 pages, 8 figures, LaTeX; final publication version
Scientific paper
10.1016/0550-3213(96)00117-4
We present a self-contained analysis of theories of discrete 2D gravity coupled to matter, using geometric methods to derive equations for generating functions in terms of free (noncommuting) variables. For the class of discrete gravity theories which correspond to matrix models, our method is a generalization of the technique of Schwinger-Dyson equations and is closely related to recent work describing the master field in terms of noncommuting variables; the important differences are that we derive a single equation for the generating function using purely graphical arguments, and that the approach is applicable to a broader class of theories than those described by matrix models. Several example applications are given here, including theories of gravity coupled to a single Ising spin ($c = 1/2$), multiple Ising spins ($c = k/2$), a general class of two-matrix models which includes the Ising theory and its dual, the three-state Potts model, and a dually weighted graph model which does not admit a simple description in terms of matrix models.
Carroll Sean M.
IV Washington Taylor
Ortiz Miguel E.
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