Analysis of a Zero of a Beta Function Using All-Orders Summation of Diagrams

TL;DR

This paper introduces a novel method for locating zeros of beta functions by summing diagrams to all orders, demonstrating improved accuracy over traditional loop calculations in supersymmetric gauge theories.

Contribution

It presents a new all-orders diagrammatic summation technique for beta functions, enhancing zero predictions in supersymmetric gauge theories compared to conventional methods.

Findings

Better agreement with exact results in supersymmetric theories

Effective in theories where partial all-orders summation is feasible

Applicable to various field theories

Abstract

Conventionally, one calculates a zero in a beta function by computing this function to a given loop order and solving for the zero. Here we discuss a different method which is applicable in theories where one can perform a partial diagrammatic summation to infinite-loop order. We show that this method, compared with the conventional method, yields much better agreement with exact results in the case of an asymptotically free gauge theory with ${\cal N}=1$ supersymmetry. Applications to other field theories are also discussed.