Conformal Geometry Program Lecture Series: Jesper Jacobsen, ENS Paris

Jesper Jacobsen, ENS Paris

Title: Logarithmic Correlations in Geometrical Critical Phenomena, Part II
Speaker:  Jesper Jacobsen, ENS Paris
Date: Thursday, February 7, 2013
Time: 11:30:00pm – 1:00pm
Place: Seminar Room 313, Simons Center





Abstract: In a critical theory correlation functions have a power law dependence on distance. In so-called logarithmic conformal field theories (LCFT) the behavior can be logarithmic as well.

In the first lecture (on Wednesday) we give a gentle introduction to some aspects of LCFT in two dimensions. We review in particular how logarithms emerge as a resonance phenomenon between two or more operators with colliding critical exponents. In this setup LCFT are produced rather simply as appropriate limits of ordinary CFT. We show how the logarithmic couplings (also known as indecomposability parameters) can be computed from this limiting procedure. We also illustrate the ubiquity of LCFT in the statistical mechanics of geometrical critical phenomena. The links with more algebraic approaches are briefly sketched.

In the second lecture (on Thursday) we show that logarithms appear as well in more than two dimensions. We illustrate this within the Potts model and its special cases, such as bond percolation. Simple representation theoretical tools are used to provide a clear geometrical interpretation of various logarithmic correlation functions. In particular we compute the logarithmic structure of two and three-point functions in arbitrary dimension.