Lecturers
Jens Braun, Technische Universität Darmstadt, Darmstadt, Germany
Léonie Canet, Université Grenobles Alpes, Grenoble, France
Laura Classen, MPI Stuttgart, Stuttgart, Germany
Bertand Delamotte, Sorbonne Université & CNRS, Paris, France
Astrid Eichhorn, Heidelberg University, Heidelberg, Germany
Holger Gies, Friedrich Schiller University Jena, Jena, Germany
Matthieu Tissier, Sorbonne Université, Paris, France
Nicolas Wschebor, Universidad de la República, Montevideo, Uruguay
Schedule
Q = question
| First week | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
| 7:45-8:30 | Breakfast | Breakfast | Breakfast | Breakfast | Breakfast | Breakfast |
| 8:45-10:15 | Delamotte 1 | Delamotte 3 | Wschebor 1 | Canet 2 | Wschebor 2 | |
| 10:45-12:15 | Delamotte 2 | Delamotte 4 | Canet 1 | Tissier | Canet 3 | |
| 12:30-13:30 | Lunch | Lunch | Lunch | Lunch | Lunch | |
| 15:00-17:30 | Arrival | |||||
| 17:00-18:00 | Tutorial | Tutorial | Tutorial | Tutorial | ||
| 18:00-19:00 | Tutorial | Tutorial | Tutorial | Tutorial | ||
| 19:30-20:30 | Dinner | Dinner | Dinner | Dinner | Dinner | |
| 20:30-22:00 | Flash talks | Q session | Posters |
| Second week | Monday | Tuesday | Wednesday | Thursday | Friday |
| 7:45-8:30 | Breakfast | Breakfast | Breakfast | Breakfast | Breakfast |
| 8:45-10:15 | Classen 1 | Gies 2 | Braun 1 | Eichhorn 2 | Braun 2 |
| 10:45-12:15 | Gies 1 | Classen 2 | Eichhorn 1 | Classen 3 | Eichhorn 3 |
| 12:30-13:30 | Lunch | Lunch | Lunch | Lunch | Lunch |
| 13:30-15:00 | Departure | ||||
| 17:00-18:00 | Tutorial | Tutorial | Tutorial | ||
| 18:00-19:00 | Tutorial | Tutorial | Tutorial | ||
| 19:30-20:30 | Dinner | Dinner | Dinner | Dinner | |
| 20:30-22:00 | Flash talks | Q session | Posters |
1) FRG basics [6 hours]: Bertrand Delamotte
The fundamental tools of the method are explained using the simple example of φ4 theory and of the Ising model. The course outline is as follows:
- Introduction to phase transitions, universality, scaling, critical exponents
- The basics of statistical field theory: effective action, mean field approximation
- The exact Wetterich RG flow equation of the effective average action
- Some approximation schemes: the Derivative Expansion, the BMW method
- Fixed points, relation with the 4-ε, 2+ε and large N expansions
- Beyond the LPA: convergence of the DE, optimization, BMW
2) Statistical physics [4.5 hours]: Nicolas Wschebor & Matthieu Tissier
The aim of this course is to show, in some explicit examples, how FRG is used and what kinds of results can be obtained. We will focus on frustrated systems and the Potts model (first lecture) and disordered systems (second lecture). During the last lecture we will discuss the more methodological problem of conformal invariance in the FRG formalism.
3) Out-of-equilibrium statistical mechanics [4.5 hours]: Léonie Canet
- Introduction to non-equilibrium critical phenomena and paradigmatic examples
- FRG formalism for non-equilibrium systems: Martin-Siggia-Rose and Keldysh field theory
- The Kardar-Parisi-Zhang equation and its strong-coupling fixed point
- The incompressible Navier-Stokes equation: fixed point and exact closure in the large momentum limit
4) Quantum condensed matter [4.5 hours]: Laura Classen
The course gives an overview of the FRG approach to fermion systems with a focus on applications in quantum materials. The content includes
- The exact renormalization group equation including bosons and fermions
- Truncation schemes (derivative and vertex expansion) and momentum resolution of the effective interaction (patch- vs. TU-FRG)
- Identifying competing orders and superconducting mechanisms
- Fermionic quantum critical points and universal behavior
5) High-energy physics [6 hours]: Jens Braun & Holger Gies
- Quantum gauge theories for particle physics
- Functional renormalization group techniques for gauge theories
- Chiral symmetry breaking and mass generation
- Phases of strong interaction physics
- Renormalization flow of the electro-weak Higgs sector
- Towards a high-energy completion of particle physics models
6) Quantum gravity [4.5 hours]: Astrid Eichhorn
- Introduction to the problem of quantum gravity
- Key concepts of asymptotic safety
- Functional Renormalization Group techniques for gravity
- Overview of the theoretical evidence for asymptotic safety in gravity
- Phenomenology of asymptotic safety in cosmology, black holes and particle physics
- Open problems that require more research