Ultraviolet to Infrared Evolution and Nonperturbative Behavior of $\mathrm{SU}(N)\otimes \mathrm{SU}(N-4)\otimes \mathrm{U}(1)$ Chiral Gauge Theories

Abstract

We analyze the ultraviolet to infrared evolution and nonperturbative properties of asymptotically free $\mathrm{SU}(N)\otimes \mathrm{SU}(N-4)\otimes \mathrm{U}(1)$ chiral gauge theories with $N_f$ copies of chiral fermions transforming according to $([2{]}_N,1{)}_{N-4}+([\bar{1}{]}_N,[\bar{1}{]}_{N-4}{)}_{-(N-2)}+(1,(2{)}_{N-4}{)}_N$, where $[k{]}_N$ and $(k{)}_N$ denote the antisymmetric and symmetric rank-$k$ tensor representations of SU($N$) and the rightmost subscript is the U(1) charge. We give a detailed discussion for the lowest nondegenerate case, $N=6$. These theories can exhibit both self-breaking of a strongly coupled gauge symmetry and induced dynamical breaking of a weakly coupled gauge interaction symmetry due to fermion condensates produced by a strongly coupled gauge interaction. A connection with the dynamical breaking of $\mathrm{SU}(2{)}_L\otimes \mathrm{U}(1{)}_Y$ electroweak gauge symmetry by the quark condensates $⟨\bar{q}q⟩$ due to color SU(3)${}_c$ interactions is discussed. We also remark on direct-product chiral gauge theories with fermions in higher-rank tensor representations.

Comments: 22 pages, latex