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 N-c(2)) such as quarks with "a" fundamental indices with a >= 3. A smooth and nontrivial N-c limit can be obtained if y(2)N(c)(a-1) is held fixed instead of the standard 't Hooft coupling g(2)N(c) as N-c -> infinity 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-c(2) and hence are not ultraviolet complete. However in lower space time dimensions ( 2+ 1, 1+1) for any Nc 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 N-c(2-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.