Effective potentials and vacuum structure in N = 1 supersymmetric gauge theories
Abstract
We derive the exact effective superpotential in 4d, N = 1 supersymmetric SU(2) gauge theories with N_{A} triplets and 2N _{ƒ} doublets of matter superfields. We find the quantum vacua of these theories; the equations of motion (for N_{A} = 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 N_{c} > 2, we derive the exact effective superpotential in branches of supersymmetric SU( N_{c}) gauge theories with one supermultiplet in the adjoint representation ( N_{A} = 1) and zero or one flavor ( N _{ƒ} = 0,1 ). We find the quantum vacua of these theories; the equations of motion can be reorganized into the singularity conditions of a genus N_{c}  1 hyperelliptic curve. Finally, we present the effective superpotential in the N _{aA}, N _{ƒ} < N _{c} cases.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1996
 DOI:
 10.1016/05503213(95)005641
 arXiv:
 arXiv:hepth/9509130
 Bibcode:
 1996NuPhB.459..160E
 Keywords:

 High Energy Physics  Theory
 EPrint:
 62 pages