Tuesday 2:00 - 3:15, South Hall 4607
Friday 11:00 - 12:15, South Hall 6635
Instructor: Sergei Gukov
Office hours: Thursday 1:00-2:00pm
Abstract:
Topological field theories are the simplest examples of quantum field
theories which, in a sense, are exactly solvable and generally covariant.
During the past twenty years they have been the main source of interaction
between physics and mathematics, which has been extremely fruitful for
both fields. Thus, ideas from gauge theory led to the discovery of new
topological invariants for 3-manifolds and 4-manifolds. By now,
topological quantum field theory (TQFT) has evolved in a vast subject,
and the main goal of this course is to give an accessible introduction
to this elegant subject.
Prerequisites:
The course will be aimed at intermediate level graduate students,
who are familiar with the basics of topology, quantum mechanics,
and classical field theory; no advanced knowledge of quantum field
theory (or string theory) is required.
In fact, the first part of the course
will include a brief introduction to supersymmetry, and various
concepts from topology will be ``rediscovered'' during the course.
Both physics and math graduate students are invited!
A rough outline of the course:
supersymmetric quantum mechanics as the simplest example of a TQFT
2D topological sigma-model
topological twist
algebraic structure and axioms of TQFT
3D Chern-Simons-Witten theory: invariants of knots and 3-manifolds
4D topological gauge theory and invariants of 4-manifolds (Donaldson and Seiberg-Witten invariants)
recent developments
Further Reading:
In order to keep the course short and self-contained, part of the material
will be taken from the original papers, such as the pioneering work of Witten:
E. Witten, Supersymmetry and Morse Theory, J.Diff.Geom. 17 (1982) 661.
