ar X iv : h ep - t h / 06 04 06 5 v 3 1 9 M ar 2 00 7 1 Phase Structure of the Large - N Reduced Gauge Theory and the Generalized Weingarten Model

Phase Structure of the Large-N Reduced Gauge Theory and the Generalized Weingarten Model Masanori Hanada1, ∗), Takashi Kanai1, ∗∗), Hikaru Kawai1,2, ∗∗∗), and Fukuichiro Kubo1, †) 1Department of Physics, Kyoto University, Kyoto 606-8502, Japan 2 Theoretical Physics Laboratory, RIKEN, Wako 351-0198, Japan (Received April 9, 2006) We study a generalization of the Weingarten model reduced to a point, which becomes the large-N reduced U(N) gauge theory in a special limit. We find that the U(1) symmetries are broken one by one, and subsequently restored as U(1) → U(1) → · · · → U(1) → 1 → U(1) as we change the coupling constants. In this model, we can develop an efficient algorithm, and we can clearly see the phase structure of the large-N reduced model. We thus conclude that this model would be useful for the study of the unitary model.