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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:

Online references:

The String Theory Wiki: Link

There’s a good lit. review by Petr Horava at Berkeley:

References for Physics 230A

References and reading assignments for Physics 230B

Website for Advanced Stat Mech at U Colorado

Papers:

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


Books:

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

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