Dynamical Symmetry Breaking with Large Anomalous Dimension

Abstract

We give an introduction to the dynamical symmetry breaking with large anomalous dimension. This is the basis of tightly bound composite Higgs models such as walking technicolor, strong ETC technicolor and top quark condensate, which are all characterized by the large anomalous dimension, γ_m \simeq 1 (walking technicolor), 1<γ_m<2 (strong ETC technicolor) and γ_m \simeq 2 (top quark condensate) due to nontrivial short distance dynamics of the gauged Nambu-Jona-Lasinio (NJL) models (gauge theories plus four-fermion interactions). Particular emphasis will be placed on the top quark condensate in which the critical phenomenon in the gauged NJL model yields a simple reason why the top quark can have an extremely large mass compared with other quarks and leptons. Topics will also cover a recent observation that the four-fermion theory {\it in the presence of gauge interactions} (gauged NJL model) can become renormalizable and nontrivial in sharp contrast to the pure NJL model without gauge interactions. The requirement of this renormalizability/nontriviality of the gauged NJL model can be applied to the top quark condensate when the standard gauge groups are unified into a GUT with ``walking'' coupling, which then naturally leads to the top quark and the Higgs masses both around 180 GeV.