ON GAUGINO CONDENSATION WITH FIELD-DEPENDENT GAUGE COUPLINGS

TL;DR

This paper analyzes gaugino condensation in supersymmetric Yang-Mills theories with field-dependent gauge couplings, deriving effective actions and potentials, and applying results to string theory models.

Contribution

It provides a detailed derivation of the low-energy Wilson and effective actions for gaugino condensation, including the superpotential and K"ahler potential, using symmetry and effective field theory methods.

Findings

Derived the Wilson action and effective superpotential for gaugino condensation.

Included string moduli dependence in the super- and K"ahler potentials.

Extended the Veneziano-Yankielowicz approach with a firmer 2PI effective action foundation.

Abstract

We study in detail gaugino condensation in globally and locally supersymmetric Yang-Mills theories. We focus on models for which gauge-neutral matter couples to the gauge bosons only through nonminimal gauge kinetic terms, for the cases of one and several condensing gauge groups. Using only symmetry arguments, the low-energy expansion, and general properties of supersymmetry, we compute the low energy Wilson action, as well as the (2PI) effective action for the composite {\it classical} superfield $U\equiv\langle \Tr\WW \rangle$, with $W_\alpha$ the supersymmetric gauge field strength. The 2PI effective action provides a firmer foundation for the approach of Veneziano and Yankielowicz, who treated the composite superfield, $U$, as a quantum degree of freedom. We show how to rederive the Wilson action by minimizing the 2PI action with respect to $U$. We determine, in both formulations and for global and local supersymmetry, the effective superpotential, $W$, the non-perturbative contributions to the low-energy K\"ahler potential $K$, and the leading higher supercovariant derivative terms in an expansion in inverse powers of the condensation scale. As an application of our results we include the string moduli dependence of the super- and K\"ahler potentials for simple orbifold models.