An Exact Elliptic Superpotential for N=1^* Deformations of Finite N=2 Gauge Theories

Abstract

We study relevant deformations of the N=2 superconformal theory on the world-volume of N D3 branes at an A_{k-1} singularity. In particular, we determine the vacuum structure of the mass-deformed theory with N=1 supersymmetry and show how the different vacua are permuted by an extended duality symmetry. We then obtain exact, modular covariant formulae (for all k, N and arbitrary gauge couplings) for the holomorphic observables in the massive vacua in two different ways: by lifting to M-theory, and by compactification to three dimensions and subsequent use of mirror symmetry. In the latter case, we find an exact superpotential for the model which coincides with a certain combination of the quadratic Hamiltonians of the spin generalization of the elliptic Calogero-Moser integrable system.

55 pages, 5 figures, latex with JHEP.cls

Cited by in corpus (33)

• Matrix Models, Geometric Engineering and Elliptic Genera
• S-duality of the Leigh-Strassler Deformation via Matrix Models
• Exact Superpotentials from Matrix Models
• Quantum moduli spaces from matrix models
• Holography for $\mathcal{N}=1^{\ast }$ on $S^4$
• Massive Vacua of N=1* Theory and S-duality from Matrix Models
• Orbifolds and Flows from Gauged Supergravity
• The Curve of Compactified 6D Gauge Theories and Integrable Systems
• N=1 Geometries via M-theory
• Non-invertible symmetries along 4d RG flows
• A 5d/3d duality from relativistic integrable system
• Five-Dimensional Gauge Theories and Quantum Mechanical Matrix Models
• N=1 Field Theories and Fluxes in IIB String Theory
• Factorization of Seiberg-Witten Curves and Compactification to Three Dimensions
• N=1* vacua, Fuzzy Spheres and Integrable Systems
• Nonperturbative Superpotentials and Compactification to Three Dimensions
• Geometric construction of elliptic integrable systems and N=1^* superpotentials
• Critical Points of Glueball Superpotentials and Equilibria of Integrable Systems
• New Results from Glueball Superpotentials and Matrix Models: the Leigh-Strassler Deformation
• D3 instantons in Calabi-Yau orientifolds with(out) fluxes
• Resurgence in the Bi-Yang-Baxter Model
• Two-Dimensional Gauge Theory and Matrix Model
• World-sheet Instantons via the Myers Effect and N=1^* Quiver Superpotentials
• N=1 G_2 SYM theory and Compactification to Three Dimensions
• Classical Spin Chains and Exact Three-dimensional Superpotentials
• On Effective Superpotentials and Compactification to Three Dimensions
• The Phase Structure of Mass-Deformed SU(2)xSU(2) Quiver Theory
• Solving matrix models using holomorphy
• Vacua of N=1 Supersymmetric QCD from Spin Chains and Matrix Models
• Solution of quantum integrable systems from quiver gauge theories
• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
• Inherited Duality and Quiver Gauge Theory
• Global variants of $\mathcal{N}=1^{\ast }$ theories and Calogero-Moser systems