Supersymmetric Models with Product Groups and Field Dependent Gauge Couplings

TL;DR

This paper investigates the dilaton-dependent effective actions in supersymmetric product group models, analyzing confining and Coulomb phases, and emphasizing the importance of proper moduli identification for physical consistency.

Contribution

It provides explicit superpotential expressions for N=1 SU(N1) x SU(N2) models with matter, highlighting the role of elliptic curves in Coulomb phases and clarifying moduli space parameterization.

Findings

Coulomb phase gauge coupling expressed via elliptic curve modulus

Dilaton superpotential exhibits runaway behavior in confining phase

Proper moduli choice is crucial for physical viability

Abstract

We study the dilaton-dependence of the effective action for N=1, SU(N1) x SU(N2) models with one generation of vectorlike matter transforming in the fundamental of both groups. We treat in detail the confining and Coulomb phases of these models writing explicit expressions in many cases for the effective superpotential. We can do so for the Wilson superpotentials of the Coulomb phase when N2=2, N1=2,4. In these cases the Coulomb phase involves a single U(1) gauge multiplet, for which we exhibit the gauge coupling in terms of the modulus of an elliptic curve. The SU(4) x SU(2) model reproduces the weak-coupling limits in a nontrivial way. In the confining phase of all of these models, the dilaton superpotential has a runaway form, but in the Coulomb phase the dilaton enjoys flat directions. Had we used the standard moduli-space variables: Tr M^k, k=1,..., N2, with M the quark condensate matrix, to parameterize the flat directions instead of the eigenvalues of M, we would find physically unacceptable behaviour, illustrating the importance to correctly identify the moduli.