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首页> 外文期刊>Physical review, D. Particles, fields, gravitation, and cosmology >Higher-loop calculations of the ultraviolet to infrared evolution of a vectorial gauge theory in the limit N_c→∞, N _f→∞ with N_f/N_c fixed
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Higher-loop calculations of the ultraviolet to infrared evolution of a vectorial gauge theory in the limit N_c→∞, N _f→∞ with N_f/N_c fixed

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摘要

We consider an asymptotically free vectorial SU(N_c) gauge theory with N_f fermions in the fundamental representation and analyze higher-loop contributions to the evolution of the theory from the ultraviolet to the infrared in the limit where N_c→∞ and N _f→∞ with r=N_f/N_c a fixed, finite constant. We focus on the case where the n-loop beta function has an infrared zero, at ξ=ξ_(IR,n?), where ξ=αN_c. We give results on ξ_(IR,n?), the anomalous dimension of the fermion bilinear evaluated at ξ_(IR,n?), denoted γ _(IR,n?), and certain structural properties of the beta function, βξ. The approach to this limit is investigated, and it is shown that the leading correction terms are strongly suppressed, by the factor 1/N_c2. This provides an understanding of a type of approximate universality in calculations for moderate values of N_c and N_f, namely, that α_(IR,n?)N_c, γ_(IR,n?), and structural properties of the beta function are similar in theories with different values of N_c and N_f provided that they have similar values of N_f/N_c. We give results up to four loops for nonsupersymmetric theories and up to three loops for supersymmetric theories.

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