Effective potentials and vacuum structure in N = 1 supersymmetric gauge theories

Shmuel Elitzura, Avraham Forge, Amit Giveon, Eliezer Rabinovici*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

We derive the exact effective superpotential in 4d, N = 1 supersymmetric SU(2) gauge theories with NA triplets and 2Nf doublets of matter superfields. We find the quantum vacua of these theories; the equations of motion (for NA = 1) can be reorganized into the singularity conditions of an elliptic curve. From the phase transition points to the Coulomb branch, we find the exact Abelian gauge couplings, τ, for arbitrary bare masses and Yukawa couplings. We thus derive the result that τ is a section of an SL(2, ℤ) bundle over the moduli space and over the parameters space of bare masses and Yukawa couplings. For Nc > 2, we derive the exact effective superpotential in branches of supersymmetric SU(Nc) gauge theories with one supermultiplet in the adjoint representation (NA = 1 ) and zero or one flavor (Nf = 0,1). We find the quantum vacua of these theories; the equations of motion can be reorganized into the singularity conditions of a genus Nc - 1 hyperelliptic curve. Finally, we present the effective superpotential in the NA, Nf < Nc cases.

Original languageAmerican English
Pages (from-to)160-206
Number of pages47
JournalNuclear Physics B
Volume459
Issue number1-2
DOIs
StatePublished - 15 Jan 1996

Bibliographical note

Funding Information:
We thank N. Seiberg for discussions. The work of SE is supported in part by the BRF - the Basic Research Foundation. The work of AG is supported in part by BSF-American-Israel Bi-National Science Foundation, by the BRF, and by an Alon fellowship. The work of ER is supported in part by BSF and by the BRF.

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