Spectral Networks
Bridging Higher-rank Teichmüller Theory and BPS States
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Beschreibung
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 Θ-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 determining and analyzing BPS spectra in class S theories is then examined. The final chapter outlines recent applications of spectral networks across a range of contemporary research areas.
This volume is intended for researchers and advanced students in either mathematics or physics who wish to enter the field.
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 Θ-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 determining and analyzing BPS spectra in class S theories is then examined. The final chapter outlines recent applications of spectral networks across a range of contemporary research areas.
This volume is intended for researchers and advanced students in either mathematics or physics who wish to enter the field.
This book is open access, which means that you have free and unlimited access Provides the necessary background to enter the rapidly expanding field of spectral networks Includes a comprehensive introduction to higher-rank Teichmüller theory and theories in class S Offers an interdisciplinary perspective at the intersection of mathematics and theoretical physics
Autor*in
Clarence Kineider
Themen in »Spectral Networks«
Open Access Spectral networks Character varieties and moduli spaces of flat connections Higher-rank Teichmüller theory Cluster varieties Supersymmetric gauge theories Seiberg-Witten theory Class S theories Fock-Goncharov theory Moduli spaces of flat connections Electric-magnetic duality