Chern-Simons Theory and Equivariant Factorization Algebras

ISBN-13: 9783658253370 / Angielski / Miękka / 2019 / 154 str.

Corina Keller

Opis

Corina Keller studies non-perturbative facets of abelian Chern-Simons theories. This is a refinement of the entirely perturbative approach to classical Chern-Simons theory via homotopy factorization algebras of observables that arise from the associated formal moduli problem describing deformations of flat principal bundles with connections over the spacetime manifold. The author shows that for theories with abelian group structure, this factorization algebra of classical observables comes naturally equipped with an action of the gauge group, which allows to encode non-perturbative effects in the classical observables.About the Author:Corina Keller currently is a doctoral student in the research group of Prof. Dr. Damien Calaque at the Université Montpellier, France. She is mostly interested in the mathematical study of field theories. Her master's thesis was supervised by PD Dr. Alessandro Valentino and Prof. Dr. Alberto Cattaneo at Zurich University, Switzerland.

Recenzje

"This book is very valuable as a guide to the mathematics needed for and going into Chern-Simons theory. ... I think this is a fabulous book, and Keller should be applauded for having written a magnificent master's thesis." (Michael Berg, MAA Reviews, August 04, 2019)

Spis treści

Gauge Theory.- Differential Graded Algebras.- Differential Graded Lie Algebras and Derived Deformation Theory.- Factorization Algebras.- Equivariant Factorization Algebras from Abelian Chern-Simons Theory.

O autorze

Corina Keller currently is a doctoral student in the research group of Prof. Dr. Damien Calaque at the Université Montpellier, France. She is mostly interested in the mathematical study of field theories. Her master’s thesis was supervised by PD Dr. Alessandro Valentino and Prof. Dr. Alberto Cattaneo at Zurich University, Switzerland.

Blurb

Corina Keller studies non-perturbative facets of abelian Chern-Simons theories. This is a refinement of the entirely perturbative approach to classical Chern-Simons theory via homotopy factorization algebras of observables that arise from the associated formal moduli problem describing deformations of flat principal bundles with connections over the spacetime manifold. The author shows that for theories with abelian group structure, this factorization algebra of classical observables comes naturally equipped with an action of the gauge group, which allows to encode non-perturbative effects in the classical observables.

Contents

• Gauge Theory
  
• Differential Graded Algebras
  
• Differential Graded Lie Algebras and Derived Deformation Theory
  
• Factorization Algebras
  
• Equivariant Factorization Algebras from Abelian Chern-Simons Theory
  

Target Groups

Scientists and students in the field of mathematical physics, theoretical physics and especially mathematics with focus on homotopy theory and homological algebra

About the Author

Corina Keller currently is a doctoral student in the research group of Prof. Dr. Damien Calaque at the Université Montpellier, France. She is mostly interested in the mathematical study of field theories. Her master’s thesis was supervised by PD Dr. Alessandro Valentino and Prof. Dr. Alberto Cattaneo at Zurich University, Switzerland.