Topical School 2011
Applications modernes de l'invariance conforme/Modern applications of conformal invariance
Nancy, March, 21st - 23rd, 2011
|
Schedule
| Monday March 21 |
|---|
| 08:45 - Welcome coffee |
| 09:00 - Michel Bauer, A short introduction to critical interfaces in 2D (1) |
| 11:00 - Andrea Gambassi, Field-theoretical description of non-equilibrium critical phenomena (1) |
| 12:30 - Lunch |
| 14:00 - Michel Bauer, A short introduction to critical interfaces in 2D (2) |
| 16:00 - Mohammad Rajabpour, Conformal symmetry in non-local field-theories |
| Tuesday March 22 |
| 09:00 - Jesper Jacobsen, Loop models and boundary CFT (1) |
| 11:00 - Michel Bauer, A short introduction to critical interfaces in 2D (3) |
| 12:30 - Lunch |
| 14:00 - Andrea Gambassi, Field-theoretical description of non-equilibrium critical phenomena (2) |
| 16:00 - Christophe Chatelain, Numerical study of Schramm-Loewner Evolution in the random 3-state Potts model. |
| Wednesday March 23 |
| 09:00 - Andrea Gambassi, Field-theoretical description of non-equilibrium critical phenomena (3) |
| 11:00 - Jesper Jacobsen, Loop models and boundary CFT (2) |
| 12:30 - Lunch |
| 14:00 - Jesper Jacobsen, Loop models and boundary CFT (3) |
| 16:00 - Malte Henkel, On logarithmic extensions of conformal invariance and on their possible applications to non-equilibrium criitical phenomena |
Speakers
| Michel Bauer (IPhT CEA Saclay) |
|---|
| A short introduction to critical interfaces in 2D (1) |
| The purpose of these lectures is very modest. They are meant to introduce
gently to the concepts of Loewner chains, local growth and stochastic
Loewner evolutions (SLEs). These concepts have played an important
role in physics and mathematics during the recent years.
The 1st chapter describes two discrete examples, the exploration process and loop-erased random walks. It can be read almost without any prerequisites. The aim is to show that even for curves de ned purely in geometrical terms, it is useful to have a statistical mechanics viewpoint where the measure on curves is derived from a measure on local degrees of freedom of some model. A third model, DLA is also introduced. The second chapter introduces Loewner chains and their relevance for the description of growth processes. A prerequisite is a minimal knowledge of complex analysis. The third chapter contains the derivation of the relevance of SLE in the description of interfaces when two properties, conformal invariance and the domain Markov property, are assumed/proved. |
| A short introduction to critical interfaces in 2D (2) |
| A short introduction to critical interfaces in 2D (3) |
| Christophe Chatelain |
| Numerical study of Schramm-Loewner Evolution in the random 3-state Potts model. |
| Andrea Gambassi (SISSA Trieste) |
| Field-theoretical description of non-equilibrium critical phenomena (1) |
| Field-theoretical description of non-equilibrium critical phenomena (2) |
| Field-theoretical description of non-equilibrium critical phenomena (3) |
| Malte Henkel |
| On logarithmic extensions of conformal invariance and on their possible applications to non-equilibrium criitical phenomena |
| A short introduction will be given to simple extensions of conformal invariance, which can be used to describe situations, where the two-point functions of a critical system also contain
additional logarithmic factors.
In particular, we shall comment on how such a construction can be extended to variants of conformal symmetry which might be useful in the description of non-equilibrium critical points, as they arise for example in ageing phenomena far from equilibrium. As an example, we shall consider critical directed percolation. |
| Jesper Jacobsen (LPT ENS Paris) |
| Loop models and boundary CFT (1) |
| The guiding principle of these lectures is to use just a few simple models
as exploratory tools for presenting a whole range of exact techniques within
two-dimensional CFT.
We focus on two models with a particularly rich physical and mathematical content: the Q-state Potts model and the O(n) model. |
| Loop models and boundary CFT (2) |
| Loop models and boundary CFT (3) |
| Mohammad Rajabpour (SISSA Trieste) |
| Conformal symmetry in non-local field-theories |
| Non-local field-theories, as a method to describe the scaling limit of long-range interacting systems, are well-known for many years and they are much studied in statistical physics. The long-range spin systems and rough surfaces are just two examples from many that could be included. We show for a particular non-local free field-theory that it has conformal symmetry in arbitrary dimensions. Using the local field theory counterparts of these field-theories we find the Noether currents and the Ward identities of the translation, rotation and scale symmetries. The operator product expansion of the introduced energy-momentum tensor with quasi-primary fields is also investigated. We shall have a close look to the rough surfeces as a physical example for our model. |
Organizing comittee
| Malte Henkel |
| Dragi Karevski |
Our partners
 |
UFA - DFH |  |
Nancy Université - UHP |
 |
Ecole doctorale EMMA |  |
Nancy Université - INPL |
 |
Groupe de Physique Statistique |  |
Institut Jean Lamour |