Global variants of $\mathcal{N}=1^{\ast }$ theories and Calogero-Moser systems

Abstract

Global variants of four-dimensional gauge theories are specified by their spectrum of genuine Wilson-'t Hooft line operators. The choice of global variant has significant consequences when spacetime is taken to be ${\mathbb{R}}^3\times S^1$. We focus on $\mathcal{N}=1^{\ast }$ theories, which are closely connected to twisted elliptic Calogero-Moser systems. We establish, on general grounds, how this gauge-theoretic topological data manifests itself on the integrable system side by introducing a notion of global variants for complex many-body integrable systems associated with Lie algebras. Focusing on $\mathcal{N}=1^{\ast }$ theories of type $A$ and $B_2$, we elucidate the implications for the structure of gapped vacua, the emergent (generalized) symmetries realized in each vacuum, and the action of spontaneously broken modular invariance.

v1: 69 pages, 27 figures; v2: 74 pages, 27 figures, final version

References in corpus (12)

• Generalized Global Symmetries
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Kramers-Wannier-like duality defects in (3+1)d gauge theories
• Non-Invertible Duality Defects in 3+1 Dimensions
• Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions
• Non-Invertible Symmetries of $\mathcal{N}=4$ SYM and Twisted Compactification
• On Continuous 2-Category Symmetries and Yang-Mills Theory
• Non-invertible symmetries along 4d RG flows
• Superconformal index of low-rank gauge theories via the Bethe Ansatz
• When the moduli space is an orbifold: Spontaneous breaking of continuous non-invertible symmetries
• Duality and Modularity in Elliptic Integrable Systems and Vacua of N=1* Gauge Theories
• The Arithmetic of Supersymmetric Vacua