2nd semester
20 credits / 30 lectures

String theory is one of the most exciting fields in theoretical physics today and offers the potential of unifying gravity and all of the other forces of nature together with all forms of matter into one unified conceptual framework. Consequently, it has, over the past 40 years evolved into a truly interdisciplinary field assimilating knowledge ranging from differential equations to algebraic geometry (and everything in between). This course offers a pedagogical introduction to various contemporary topics in the field (and related areas) depending largely on the interests of the class. It will be broken up into three parts:

Part I: String Theory as a Conformal Field Theory 

1. The Conformal Group
2. Conformal field theory - primary fields, energy momentum tensor and radial quantisatio
3. The operator product expansion
4. Normal ordering and the CFT Hilbert space
5. Free bosons and fermions
6. Bosonisation and conformal correlators
7. Virasoro representation theory

Part II: Superconformal field theory

8. Introduction to superspace
9. N = 1 superconformal field theories
10. N = 2 superconformal field theories
11. Chiral rings and spectral flow

Part III: (optional) Advanced topics I - The 2-dimensional Ising model

12. A review of statistical mechanics and critical phenomena
13. The renormalisation group
14. Ising model correlators and bosonization revisited

Part IV: (optional) Advanced topics II - The shadow formalism

15. Superconformal symmetry in D=1 and the Casimir equation
16. Shadow representations in D=1
17. Shadow representations in D=2