Large Nc gauge theory with quarks in high representations

This paper explores a novel tractable regime for ultraviolet-complete quantum field theories—the large N_c limit of non-Abelian gauge theories with quarks in high-dimensional representations (scaling with N_c faster than Nc2), such as quarks with "a" fundamental indices with a ≥3. A smooth and nontrivial N_c limit can be obtained if ^g2Nca -1 is held fixed instead of the standard 't Hooft coupling ^g2Nc as N_c→∞ where g is the gauge coupling. SU(N_c) gauge theories in 3+1 dimensions are not asymptotically free at large N_c when they contain quarks in representations for which the dimensions scale faster than N_c² and hence are not ultraviolet complete. However, in lower space-time dimensions (2+1, 1+1), for any N_c, renormalization group flow for such theories always has a stable ultraviolet fixed point at g =0; the theory is thus ultraviolet complete. For the case of massless quarks, the theory has an infrared fixed point. For massive quarks, the theory is confining. The confining scale is parametrically of the order Nc2-a/4-d and is driven to zero at large N_c for theories with a >2 and d<4 where d is the space-time dimension.