Four chapters on low-dimensional gauge theories
2015-04-21 10:00 - 2015-04-23 12:00 | BI A0 448 https://plan.epfl.ch/?room==BI%20A0%20448
Thierry Lévy & Ambar Sengupta
1. Historical introduction : from classical electromagnetism to gauge theories
Gauge theories govern the interaction between the fundamental constituents of matter. Electromagnetism is the most familiar such theory. In this lecture we look back at Maxwell's equations for the electromagnetic field and explore how these relate to the Yang-Mills equations for gauge theories.2. A case study : two-dimensional Yang-Mills theory
In this lecture we explore the Yang-Mills measure in two dimensions. This measure arises from the study of a quantum theory for the Yang-Mills gauge field. Geometry and probability interweave in the construction and study of this measure.3. A connection with random matrix theory : the master field
Every gauge theory has associated to it a group of symmetries, typically a subgroup of U(N), the group of NxN unitary matrices. A rich structure emerges when considers the behavior of this theory as N goes to infinity. This lecture will explore results and questions in this area, which lies at the juncture of random matrix theory and stochastic geometry.4. The scale of dimensions : Yang-Mills and Chern-Simons
Chern-Simons theory is a gauge theory in three dimensions that has an elegant mathematical structure with a topological flavor. In this theory we explore aspects of Yang-Mills and Chern-Simons functional integrals from a geometric viewpoint.
