Nonperturbative Superpotentials and Compactification to Three Dimensions

Abstract

We consider four-dimensional N=2 supersymmetric gauge theories with gauge group U(N) on R^3 x S^1, in the presence of a classical superpotential. The low-energy quantum superpotential is obtained by simply replacing the adjoint scalar superfield in the classical superpotential by the Lax matrix of the integrable system that underlies the 4d field theory. We verify in a number of examples that the vacuum structure obtained in this way matches precisely that in 4d, although the degrees of freedom that appear are quite distinct. Several features of 4d field theories, such as the possibility of lifting vacua from U(N) to U(tN), become particularly simple in this framework. It turns out that supersymmetric vacua give rise to a reduction of the integrable system which contains information about the field theory but also about the Dijkgraaf-Vafa matrix model. The relation between the matrix model and the quantum superpotential on R^3 x S^1 appears to involve a novel kind of mirror symmetry.

LaTeX, 45 pages, uses AmsMath, minor correction, reference added

References in corpus (16)

• Chiral Rings and Anomalies in Supersymmetric Gauge Theory
• A Perturbative Window into Non-Perturbative Physics
• On Geometry and Matrix Models
• Perturbative Computation of Glueball Superpotentials
• Phases of N=1 Supersymmetric Gauge Theories and Matrices
• Perturbative Analysis of Gauged Matrix Models
• On Exactly Marginal Deformations of N=4 SYM and Type IIB Supergravity on AdS_5 * S^5
• Replica Limit of the Toda Lattice Equation
• N=1 Supersymmetry, Deconstruction, and Bosonic Gauge Theories
• On some integrals over the U(N) unitary group and their large N limit
• Exact Superpotentials from Matrix Models
• Gluino-Condensate (CIV-DV) Prepotential from its Whitham-Time Derivatives
• $\mathcal{N}=1$ Theories and a Geometric Master Field
• Five-Dimensional Gauge Theories and Quantum Mechanical Matrix Models
• Factorization of Seiberg-Witten Curves and Compactification to Three Dimensions
• Perturbative Derivation of Mirror Symmetry

Cited by in corpus (12)

• An Introduction to Supersymmetric Gauge Theories and Matrix Models
• Supersymmetric Quenching of the Toda Lattice Equation
• Factorization of Seiberg-Witten Curves and Compactification to Three Dimensions
• The N=1* Theories on R^{1+2} X S^1 with Twisted Boundary Conditions
• 3d Deconfinement, Product gauge group, Seiberg-Witten and New 3d dualities
• The Whitham Deformation of the Dijkgraaf-Vafa Theory
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• The Glueball Superpotential
• Improved matrix-model calculation of the N=2 prepotential
• Classical Spin Chains and Exact Three-dimensional Superpotentials
• Vacua of N=1 Supersymmetric QCD from Spin Chains and Matrix Models
• Twisted Six Dimensional Gauge Theories on Tori, Matrix Models, and Integrable Systems