Random geometry and non-unitary quantum field theories. - Département de Physique de l'Ecole Normale supérieure

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Random geometry and non-unitary quantum field theories.

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November 14 - 18, 2022 :
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Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

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Next student seminar :
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Here you can find information about your internships:
Experimental Internship - Undergraduate program
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November 14 - 18, 2022 :
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Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

Faculty : Jesper Jacobsen

ECTS credits : 3

Language of instruction : English

Examination :

Description :

This course is an introduction to random geometrical critical phenomena and their description using algebraic, probabilistic and quantum field theoretical techniques. The main objects of study are conformally invariant extended objects, such as percolation clusters, domain walls in spin systems, and self-avoiding walks. We wish to describe these objects as precisely as possible, via critical exponents and correlation functions. A substantial part of the work takes place in two dimensions, but some of the techniques can be pushed to higher dimensions as well.

After introducing the geometrical objects and their phenomenology, we describe their relations to lattice models of loops and spins. In the continuum limit we make contact with a variant of Liouville quantum field theory and other results from high-energy physics. The study of two, three and four-point correlation functions calls for ideas of fusion and conformal bootstrap. Another angle of attack is provided by probabilistic approaches, such as Stochastic Loewner Evolution (SLE) and its variants. Crucial algebraic insight is obtained by identifying the algebraic symmetries of the models, both in the lattice description (affine Temperley-Lieb algebra) and in the continuum limit (interchiral conformal symmetry). In many cases of physical interest the corresponding representations are indecomposable, so that correlation functions are described by logarithmic conformal field theories.

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Next student seminar :
Access to the program

Here you can find information about your internships:
Experimental Internship - Undergraduate program
Master ICFP first year Internship

News : ICFP Research seminars
November 14 - 18, 2022 :
All information about the program

Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr