Reduction of Dual Theories

TL;DR

This paper applies the Reduction of Couplings method to dual gauge theories with superpotentials, deriving a unique relation between superpotential and gauge couplings valid across different regimes.

Contribution

It introduces a systematic way to express superpotential parameters in terms of gauge couplings in dual theories, providing explicit solutions valid to all orders.

Findings

Unique, isolated solutions in the conformal window

Explicit expression for superpotential coupling as a function of gauge coupling

Solution validity extends to the free magnetic interval

Abstract

In view of the presence of a superpotential, the dual of a gauge theory like SQCD contains two coupling parameters. The method of the Reduction of Couplings is used in order to express the parameter of the superpotential in terms of the dual gauge coupling. In the conformal window and above it, a unique, isolated solution is obtained. The coupling parameter of the superpotential is given simply by f times the square of the gauge coupling. Here f is a function of the the number of colors and the number of flavors, and it is known explicitly. The solution is valid to all orders in the asymptotic expansion, and it is the appropriate choice for the dual theory. The same solution exists in the free magnetic interval. A `general' solution with non-integer powers is discussed, as are some exceptional cases.