Non-local Non-Abelian Gauge Theory: Conformal Invariance and $\beta$-function

Abstract

This paper focuses on extending our previous discussion of an Abelian U(1) gauge theory involving infinite derivatives to a non-Abelian SU(N) case. The renormalization group equation (RGEs) of the SU(N) gauge coupling is calculated and shown to reproduce the local theory $\beta$-function in the limit of the non-local scale M $\to \infty$. Interestingly, the gauge coupling stops its running beyond the scale $M$, approaching an asymptotically conformal theory.

Version accepted for publication in PRD. Minor changes in the text only

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