Duality in a Supersymmetric Gauge Theory From a Perturbative Viewpoint

TL;DR

This paper investigates duality in $ ext{N}=1$ supersymmetric QCD within the non-Abelian Coulomb phase using scheme-independent series expansions, revealing how key conformal data can be accurately approximated order-by-order.

Contribution

It introduces a perturbative, scheme-independent approach to analyze duality and conformal data in supersymmetric gauge theories, providing precise approximations.

Findings

Scheme-independent series expansions accurately approximate conformal dimensions.

Truncations of series yield highly precise results.

Method applies to electric and magnetic theories in supersymmetric QCD.

Abstract

We study duality in $\mathcal{N}=1$ supersymmetric QCD in the non-Abelian Coulomb phase, order-by-order in scheme-independent series expansions. Using exact results, we show how the dimensions of various fundamental and composite chiral superfields, and the quantities $a$, $a/c$, and $b$ at superconformal fixed points of the renormalization group emerge in scheme-independent series expansions in the electric and magnetic theories. We further demonstrate that truncations of these series expansions to modest order yield very accurate approximations to these quantities.