Large Nc gauge theory with quarks in high representations

Abstract

This paper explores a novel tractable regime for ultraviolet-complete quantum field theories -- the large Nc limit of non-abelian gauge theories with quarks in high dimensional representations (scaling with Nc faster than Nc^2 ), such as quarks with 'a' fundamental indices with a greater than or equal to 3. A smooth and nontrivial Nc limit can be obtained if g^2 Nc^(a-1) is held fixed instead of the standard t Hooft coupling g^2 Nc as Nc goes to infinity where g is the gauge coupling. SU(Nc) gauge theories in 3+1 dimensions are not asymptotically free at large Nc when they contain quarks in representations whose dimensions scale faster than Nc^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 Nc^((2-a)/(4-d)) and is driven to zero at large Nc for theories with a > 2 and d < 4 where d is the space time dimension.