PHY 622 & 623 String Theory I & II

F'16, MWF 9:00-53 (P125) — S'17, MWF 10:00-53 (P128)

C. Herzog, M. Roček, W. Siegel (, P. van Nieuwenhuizen -- fall only)

office consultation available on request

This is a two-semester course. The course is taught by all of us; we sit in each other's lectures, and encourage discussions with students.

String theory is a vast subject, so it is not possible to cover all areas. We give simple introductions to the main areas; the lectures are self-contained, and typed notes will be distributed. We do not use phrases like "It can be shown that...", but rather do all derivations and calculations explicitly.

Prerequisites

It would be useful to be familiar with
  1. quantum field theory of the Standard Model
  2. general relativity (& its coupling to the Standard Model)
but we will fit the course to the students' background.

Grading

Grading is S/U, determined completely by the final exam, which is part written & part oral.

First semester

  1. Free bosonic strings: What are strings? Action, quantization, spectrum, BRST charge, D = 26
  2. Why strings?
  3. Free spinning strings: rigid supersymmetry and supergravity in two dimensions, extensions of the results of the bosonic string
  4. Conformal and superconformal field theory
  5. Tree graphs in bosonic string theory
  6. Tree graphs in spinning string theory, picture changing
  7. Differential geometry and supersymmetric vacuua

Second semester

This semester, we start by discussing BPS states in supergravity theories and relating them to D-branes in string theory. We then consider the near horizon limit and develop the AdS/CFT correspondence, with a new emphasis on diverse applications to a variety of systems, including condensed matter and nuclear physics.

After a detailed introduction of the necessary concepts, we obtain the maximally supersymmetric supergravity theory in 4+1 dimensions from the IIB supergravity theory in 9+1 dimensions by applying the dimensional reduction method of Nordström, Kaluza, Klein and others.

Other topics to be covered are a basic self-contained introduction to manifolds and string compactification.

If time permits, we shall also give an introduction to the heterotic string. This requires some basic results of group theory--representations of SO(N) and E₈ -- which will be carefully explained.

Though the semester will build on the basics introduced last semester as well as aspects of supergravity introduced in Prof. van Nieuwenhuizen's parallel course, we shall make every attempt to make the new material understandable in its own right -- particularly the applications of the AdS/CFT correspondence.

On-line lecture notes

Herzog's lectures

Siegel's lectures (from Fields v4)

Outlines of Siegel's lectures from previous semesters:

but sometimes extra bits were taken from:

Some related group theory notes by van Nieuwenhuizen

 

University-required statements
These statements are required in all University syllabi. (They are the same in all course syllabi, so just read it once.)