Renormalization Group Approach to Matrix Models and Vector Models

Details Renormalization Group Approach to Matrix Models and Vector Models Renormalization Group Approach to Matrix Models and Vector Models

1993-07-26

arxiv.org/abs/hep-th/9307154v2

Prog.Theor.Phys.Suppl.114:53-71,1993

Physics

High Energy Physics

High Energy Physics - Theory

Talk at the workshop "Quantum Gravity", Yukawa Institute, Kyoto, Nov. 1992, LaTeX, 22 pages + 3 Postscript figures (included i

Scientific paper

10.1143/PTPS.114.53

The renormalization group approach is studied for large $N$ models. The approach of Br\'ezin and Zinn-Justin is explained and examined for matrix models. The validity of the approach is clarified by using the vector model as a similar and simpler example. An exact difference equation is obtained which relates free energies for neighboring values of $N$. The reparametrization freedom in field space provides infinitely many identities which reduce the infinite dimensional coupling constant space to that of finite dimensions. The effective beta functions give exact values for the fixed points and the susceptibility exponents. A detailed study of the effective renormalization group flow is presented for cases with up to two coupling constants. We draw the two-dimensional flow diagram.

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