Magnetic S-parameter

TL;DR

This paper computes the S-parameter in both electric and magnetic descriptions of nonsupersymmetric gauge theories to test gauge duality and explore the conformal window, providing a nonperturbative quantity relevant for understanding gauge duals.

Contribution

It presents the first explicit nonperturbative computation of the S-parameter in electric variables using gauge duality in nonsupersymmetric theories, supporting a universal lower bound.

Findings

Magnetic S-parameter has a simple expression at the lower conformal bound.

Results support a universal lower bound on the S parameter.

The S-parameter can be used to identify gauge duals and count degrees of freedom.

Abstract

We propose a direct test of the existence of gauge duals for nonsupersymmetric asymptotically free gauge theories developing an infrared fixed point by computing the S-parameter in the electric and dual magnetic description. In particular we show that at the lower bound of the conformal window the magnetic S-parameter, i.e. the one determined via the dual magnetic gauge theory, assumes a simple expression in terms of the elementary magnetic degrees of freedom. The results further support our recent conjecture of the existence of a universal lower bound on the S parameter and indicates that it is an ideal operator for counting the active physical degrees of freedom within the conformal window. Our results can be directly used to unveil possible four dimensional gauge duals and constitute the first explicit computation of a nonperturbative quantity, in the electric variables, via nonsupersymmetric gauge duality.