The goal of the course is to introduce perturbative string theory, which to date is the only consistent theory of quantum gravity. While much of current research focuses on non-perturbative issues, string perturbation theory provides the backbone of the subject, and is likely to re-emerge as a useful tool when more speculative directions become quantitative. A secondary goal is introducing techniques such as conformal field theory or quantization of gauge systems, which are useful in their own right.
The main source for the course is "String Theory", volume 1, by Joe Polchinski. I will follow it in more or less the same order as the excellent lecture notes provided by David Tong, but will chart my own course within each subject. Even just perturbative string theory is a very large subject, tied to many corners in theoretical physics. I am likely to use many more resources, which I will refer to as needed.
Rough outline of the course is as follows:
-- Historical overview, the context of string perturbation theory.
-- Worldline formulation of classical and quantum field theory.
-- Moving to worldsheets: string action and symmetries.
-- The string spectrum, open and closed.
-- Conformal field theory.
-- Polyakov path integral.
-- String interactions and scattering amplitudes.
-- Effective actions.
-- T-duality.
As this is a specialized graduate course, there will be a large component of independent study. I will assign readings from the lecture notes, and will use my lecture time to provide details and expand on the notes in different directions. I will also recommend papers for further study and exercises which can help deepen the understanding of the subjects discussed in class.