TL;DR
This paper surveys recent developments in supergroup gauge theory, covering supermatrix models, four-dimensional Yang--Mills with supergroup symmetry, and their non-perturbative aspects like instantons and Seiberg-Witten geometry.
Contribution
It provides a comprehensive overview of supergroup gauge theories, highlighting new insights into their geometric, algebraic, and non-perturbative properties.
Findings
Supermatrix models serve as toy models for supergroup gauge theories.
Non-perturbative analysis reveals rich structures like instantons and Seiberg-Witten solutions.
Connections to intersecting defects and Bethe/gauge correspondence are explored.
Abstract
We provide a survey of recent studies of supergroup gauge theory. We first discuss supermatrix model as a zero-dimensional toy model of supergroup gauge theory and its geometric and algebraic characterization. We then focus on four-dimensional Yang--Mills theory with supergroup gauge symmetry and explore its non-perturbative properties, including instanton calculus, Seiberg-Witten geometry, Bethe/gauge correspondence, and its realization with intersecting defects.
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