Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-09-02
Nucl.Phys. B434 (1995) 283-318; Erratum-ibid. B441 (1995) 405
Physics
High Energy Physics
High Energy Physics - Theory
34 pages in LaTeX, 4 eps figures included in uufiled form, with a few minor but helpful corrections
Scientific paper
Large-$N$ renormalization group equations for one- and two-matrix models are derived. The exact renormalization group equation involving infinitely many induced interactions can be rewritten in a form that has a finite number of coupling constants by taking account of reparametrization identities. Despite the nonlinearity of the equation, the location of fixed points and the scaling exponents can be extracted from the equation. They agree with the spectrum of relevant operators in the exact solution. A linearized $\beta$-function approximates well the global phase structure which includes several nontrivial fixed points. The global renormalization group flow suggests a kind of $c$-theorem in two-dimensional quantum gravity.
Higuchi Saburo
Itoi Chigak
Nishigaki Shinsuke
Sakai Norisuke
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