Here’s a supremely ambitious vague plan of study for this semester. I want to spend the next 4 months thinking about some (subset) of the following things:
1. The path integral approach, and it’s relation to topics like solitons, instantons, monopoles. Applications to high energy and condensed matter.
2. Conformal field theory. Dualities. What is the ADS / CFT correspondence and the holographic principle?
3. Renormalization and the Renormalization group. Applications to high energy and condensed matter. Wilson loops. Renormalization and ricci flow.
The plan is subject to plenty of change as I piece together what’s going on. I’ll add useful references as I find them.
Here’s a collection of literature on these subjects:
The String Theory Wiki: Link
There’s a good lit. review by Petr Horava at Berkeley:
References for Physics 230A
Website for Advanced Stat Mech at U Colorado
Introduction to ADS/CFT: Link
Applied Conformal Field Theory: Link
Supersymmetric gauge theories and the ADS/CFT correspondence: Link
2D Ising model as a soluble problem of many fermions : Link
Order and disorder operators and Majorana fermions in the 2D Ising model, in Gauge Fields and Strings, by A. Polyakov, pp. 275-278
Duality in the Ising model: Link
Electromagnetic duality for children: Link
Appendix to chapter 21 in Shankar. The chapter has a nice discussion of path integrals and mentions instantons.
Quantum Field Theory in a Nutshell: A. Zee
Conformal Field Theory: Francesco, Mathieu and Senechal
Aspects of Symmetry: Sydney Coleman
Instantons and Solitons: R. Rajaraman