# 2008 Arnold Sommerfeld Summer School

(Boundary) Conformal Field Theory: Introduction and Applications

06.10.2008 – 10.10.2008

General information:

The 2008 Arnold Sommerfeld Summer School is open to all interested graduate students and postdocs that have a good knowledge of field theory, but do not know conformal field theory yet and would like to get a glimpse of what it is about. Applications will, in particular, focus on boundary conformal field theory.

The school, organized by Jan von Delft and Dieter Lüst, will take place at the Arnold Sommerfeld Center for Theoretical Physics (ASC) in the heart of the city.

There will be no conference fee.

There will be a common dinner for all the participants on Wednesday October 8.

We do advise to book accomodation as early as possible, since the canonical arrival date for the School (October 5) coincides with the last day of Munich's Oktoberfest.

Registration:

All participants are kindly requested to send a short e-mail to helling (at) theorie.physik.uni-muenchen.de with the subject: registration ASC School 2008

Lectures:

Venue: ASC, Theresienstr. 37, third floor, seminar room 348/349.

Timetable: Mo - Fr at 9:00 - 10:15, 10:45 - 12:00, 14:00 - 15:15, 15:45 - 17:00

On Day 1 (October 6): 4 introductory lectures on Conformal Field Theory

Ilka Brunner (LMU) at 9:00 - 10:15, 10:45 - 12:00, 14:00 - 15:15 :

1) Energy momentum tensor

2) Virasoro algebra

3) Highest weight states

4) Operator product expansions

5) Conformal Ward identities

6) Correlation functions

Christian Römelsberger (LMU) at 15:45 - 17:00 :

1) Torus partition functions

2) Modular invariance

On Day 2 and 3:

Andreas Recknagel (King's College London) at 10:45 - 12:00, 15:45 - 17:00 : 4 lectures on Boundary CFT

1) construction of boundary conditions: gluing conditions and symmetries of boundary CFTs

2) correlators

3) bulk and boundary OPEs

4) sewing relations, in particular Cardy condition and boundary partition function

5) boundary perturbations/deformations

6) examples: free boson, rotated boundary states, N=2 superVirasoro, WZW boundary states, D-branes

Pasquale Calabrese (University of Pisa) at 9:00 - 10:15, 14:00 - 15:15 : 4 lectures on CFT and Entanglement Entropy

Part I:

1) Introduction to Entanglement

2) Path integral formulation for the reduced density marix

3) Entanglement entropy in CFT

4) Distribution of eigenvalues of the reduced density matrix

5) The example of the XX chain

Part II:

1) Generalities of quantum quenches

2) Path integral for quantum quenches

3) CFT for a global quench

4) CFT for a local quench

5) Domain wall initial state with boundary condition changing operators

On Day 4 and 5:

Denis Bernard (Ecole Normale Superieure) at 9:00 - 10:15, 14:00 - 15:15 : 4 lectures on Stochastic Loewner Evolution

1) Discrete models and statistical interfaces

2) SLE: probabilistic description and basic properties

3) SLE/CFT correspondance and applications

4a) Off-critical SLE (tentatively)

4b) or more on applications of SLE

Jan von Delft (LMU) at 10:45 - 12:00, 15:45 - 17:00 : 3 lectures on Conformal Field Theory Solution of Kondo Model

1) Introduction to Kondo Model, mapping to a CFT

2) Algebraic computation of finite-size spectrum

3) Finite temperature properties via finite-size scaling on cylinder

Sponsors: