Breakdown of Universality in Random Matrix Models

We calculate smoothed correlators for a large random matrix model with a potential containing products of two traces \tr W_1(M) \cdot \tr W_2(M) in addition to a single trace \tr V(M). Connected correlation function of density eigenvalues receives corrections besides the universal part derived by Brezin and Zee and it is no longer universal in a strong sense.Comment: 16 pages, LaTex, references and footnote adde

W_\infty and w_\infty Gauge Theories and Contraction

We present a general method of constructing Winf and winf gauge theories in terms of d+2 dimensional local fields. In this formulation the \Winf gauge theory Lagrangians involve non-local interactions, but the winf theories are entirely local. We discuss the so-called classical contraction procedure by which we derive the Lagrangian of winf gauge theory from that of the corresponding Winf gauge theory. In order to discuss the relationship between quantum Winf and quantum winf gauge theory we solve d=1 gauge theory models of a Higgs field exactly by using the collective field method. Based on this we conclude that the Winf gauge theory can be regarded as the large N limit of the corresponding SU(N) gauge theory once an appropriate coupling constant renormalization is made, while the winf gauge theory cannot be.Comment: 21 pages, plain Te