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This chapter focuses on the general framework of 4d gauge theories with \(\mathcal N=1\) supersymmetry, of which \(\mathcal N=2\) theories form a special subset. We first discuss the symmetries that govern 4d quantum field theories, offering essential background for understanding supersymmetric models. Following this, we explore the classical properties of \(4d\mathcal N=1\) gauge theories, with particular emphasis on the construction of \(\mathcal N=1\) Lagrangian densities. Lastly, we address the quantum aspects of these theories, delving into key topics such as renormalization, anomalies, holomorphy, and quantum corrections to moduli spaces. This groundwork will prepare us for a deeper study of \(\mathcal N=2\) dynamics and, ultimately, spectral networks.

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Four-Dimensional Supersymmetric Quantum Field Theories

  • 章节

  • 出版模式：

    开放获取

  • 发表日期：

    2026年

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  • Clarence Kineider,
  • Georgios Kydonakis,
  • Eugen Rogozinnikov,
  • Valdo Tatitscheff,
  • Alexander Thomas

摘要

This chapter focuses on the general framework of 4d gauge theories with \(\mathcal N=1\) supersymmetry, of which \(\mathcal N=2\) theories form a special subset. We first discuss the symmetries that govern 4d quantum field theories, offering essential background for understanding supersymmetric models. Following this, we explore the classical properties of \(4d\mathcal N=1\) gauge theories, with particular emphasis on the construction of \(\mathcal N=1\) Lagrangian densities. Lastly, we address the quantum aspects of these theories, delving into key topics such as renormalization, anomalies, holomorphy, and quantum corrections to moduli spaces. This groundwork will prepare us for a deeper study of \(\mathcal N=2\) dynamics and, ultimately, spectral networks.