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A platform where experts in conformal bootstrap techniques and in statistical physics can discuss and solve specific mathematical and physical problems.
Week 1: Status of the conformal bootstrap
Leading experts on the conformal bootstrap will give introductory courses on:
- Conformal symmetry and conformally invariant QFTs.
- Input and output data of the conformal bootstrap.
- Analytical and numerical tools.
- Pros and cons of various techniques.
Week 2: Statistical physics targets
Discussing various statistical models, with an emphasis on the aspects that are relevant to a bootstrap approach.
- Symmetries, unitarity.
- Space of states, critical exponents, correlation functions.
- Which observables can be computed with a good precision?
- Families of models, marginal deformations, toy models.
- Outstanding physical questions, interest of the critical limit for these questions.
Examples may include: percolation, depinning, loop-erased random walks, sandpiles, Chalker-Coddington network for the integer quantum Hall effect.
Week 3: Structural phase transitions and other unitary problems
Structural phase transitions are described by unitary theories, which makes them accessible to existing numerical bootstrap methods. However, they are challenging because of their intricate group theory and phenomenology. We will review:
- Necessary group theory tools.
- Main results from the renormalization group approach.
- Experimental situation.
We will also discuss other types of unitary CFTs.
Week 4: Non-unitary bootstrap methods
The best-developed numerical bootstrap techniques rely on unitarity, which is however not available in logarithmic CFTs, the critical Potts model, percolation, or disordered systems. We will explore two approaches to the non-unitary bootstrap:
- The perturbative epsilon expansion.
- Gliozzi's method and extremal flows.
We may start with a family of unitary models such as the O(N) model, and vary the parameter continuously to a non-unitary or logarithmic fixed point.