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 $2N_f$ 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, $\tau$, for arbitrary bare masses and Yukawa couplings. We thus {\em derive} the result that $\tau$ is a section of an $SL(2,\mathbb{Z})$ 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 ($N_f=0,1$). 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 $N_A$, $N_f<N_c$ cases.

62 pages

References in corpus (15)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• Exact Results on the Space of Vacua of Four Dimensional SUSY Gauge Theories
• Exactly Marginal Operators and Duality in Four Dimensional N=1 Supersymmetric Gauge Theory
• Simple Singularities and N=2 Supersymmetric Yang-Mills Theory
• The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory
• Duality, Monopoles, Dyons, Confinement and Oblique Confinement in Supersymmetric SO(N_c) Gauge Theories
• Exact Superpotentials in Four Dimensions
• On Duality in Supersymmetric Yang-Mills Theory
• Phases of N=1 supersymmetric gauge theories in four dimensions
• A Comment on Duality in N=1 Supersymmetric Non -- Abelian Gauge Theories
• Proposal for a Simple Model of Dynamical SUSY Breaking
• ``Integrating in'' and exact superpotentials in 4d
• More Results in $N=1$ Supersymmetric Gauge Theories

Cited by in corpus (14)

• Brane Dynamics and Gauge Theory
• Type I Superconductivity upon Monopole Condensation in Seiberg-Witten Theory
• A UV complete partially composite-pNGB Higgs
• A Sequence of Duals for Sp(2N) Supersymmetric Gauge Theories with Adjoint Matter
• Gauging Flavour in Meta-Stable Susy Breaking Models
• Strings, Branes and Extra Dimensions
• Massless Monopoles Via Confining Phase Superpotentials
• M Theory, Type IIA String and 4D N=1 SUSY SU(N_L) X SU(N_R) Gauge Theory
• Landscape of Simple Superconformal Field Theories in 4d
• Confining Phase of N=1 Supersymmetric Gauge Theories and N=2 Massless Solitons
• N=2 Curves and a Coulomb Phase in N=1 SUSY Gauge Theories with Adjoint and Fundamental Matters
• The Coulomb Phase in N=1 Gauge Theories With a LG-Type Superpotenetial
• On effective superpotentials and Kutasov duality
• On mixed phases in gauge theories