Spectral Networks: Bridging Higher-rank Teichmüller Theory and BPS States (Lecture Notes in Mathematics, 2386)

This open access book offers a comprehensive introduction to spectral networks from a unified viewpoint that bridges geometry with the physics of supersymmetric gauge theories.It provides the foundational background needed to approach the frontiers of this rapidly evolving field, treating geometric and physical aspects in parallel.After surveying fundamental topics in algebra and geometry, a detailed introduction to higher-rank Teichmüller theory is developed, including Fock-Goncharov theory for Hitchin representations, maximal representations and the more recent notion of T-positivity.Spectral networks are subsequently introduced, emphasizing their utility in the study of character varieties via the abelianization and non-abelianization maps they define.In parallel, key aspects of four-dimensional gauge dynamics with eight supercharges are explored, including electric-magnetic duality, Seiberg-Witten theory, and class S theories.The role of spectral networks as a framework for determi