Physics 230B - Quantum Field Theory II,
with Emphasis on Dualities
In today's quantum field theory, dualities are everywhere. Even string
theory can be viewed as a duality.
The course will be roughly organized into five main Chapters, depending on
the type of theory considered. Along the way, we will develop some technical
tools, such as instantons, anomalies, supersymmetry etc.
(Disclaimer: The syllabus below contains a large
number of topics, many of which could individually serve as material for a
full-semester course. As a result, covering all this material will require
spending a rather limited amount of time on each topic, conveying its
"nutshell" instead of going in-depth -- kind of in the spirit of Tony Zee's
book. In particular, we will not be able to spend more than about three weeks
on each of the five Chapters. Also, the lecturer reserves the right not
to cover some of the topics listed below :-)
Chapter 0: Introduction.
Overview; introduction to some advanced techniques: Instantons, anomalies.
Chapter 1: Dualities on the lattice.
Duality in the Ising model, other spin models; dualities versus
renormalization and RG; gauge theories on the lattice; exact
solution of 2d pure-glue Yang-Mills theory.
Chapter 2: Dualities in two-dimensional QFT (in particular,
nonlinear sigma models).
Sine-Gordon/Thirring model duality; bosonization; Gross-Neveu model at
large N; basics of 2d CFT; sigma models; (gauged) WZW models;
supersymmetry in two dimensions; T-duality; mirror symmetry.
Chapter 3: Dualities in (super) Yang-Mills theories.
Supersymmetric Yang-Mills (=SYM) in 4d; electric-magnetic duality;
finiteness and conformality of N=4 SYM; Montonen-Olive duality in
N=4 SYM; the Seiberg-Witten solution of N=2 SYM; Seiberg
dualities in N=1 SYM; 't Hooft's solution of 2d QCD at large N.
Chapter 4: Gravity as an effective quantum field theory.
(This is a prerequisite for Chapter 5, as well as of independent interest
as basic background for any (future) quantum theory of gravity.)
Gravity as an effective theory; naturalness; the cosmological constant
problem. N=1 supergravity in
4d; N=8 supergravity in 4d; supergravity in 11d as effective M-theory;
supergravities in 10d: SL(2,Z) duality of IIB supergravity.
Black holes and branes; Bekenstein-Hawking entropy; holography.
Chapter 5: Field-theory/gravity dualities.
AdS/CFT correspondence; string theory as a duality.