Solution of gauge theories induced by fundamental representation scalars

Details Solution of gauge theories induced by fundamental representation scalars Solution of gauge theories induced by fundamental representation scalars

1997-09-19

arxiv.org/abs/hep-ph/9709410v1

Phys.Rev. D57 (1998) 5084-5091

Physics

High Energy Physics

High Energy Physics - Phenomenology

12 pages, LaTeX

Scientific paper

10.1103/PhysRevD.57.5084

Gauge theories induced by scalars in the fundamental representation of the $U(N_c)_{gauge}\times U(N_f)_{global}$ group are investigated in the large $N_c$ and $N_f$ limit. A master field is defined from bilinears of the scalar field following an Eguchi-Kawai type reduction of spacetime. The density function for the master field satisfies an integral equation that can be solved exactly in two dimensions (D=2) and in a convergent series of approximations at $D>2$. While at D=2 the system is in the same phase at all $\epsilon=N_c/N_f$, it undergoes a phase transition at a critical value, $\epsilon_c(D)$, for $D>2$.

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