Recent developments in conformal field theories

  title={Recent developments in conformal field theories},
  author={Seif Randjbar-Daemi and Ergin Sezgin and Jean-Bernard Zuber},
This book is related to the following topics: A case study in finite groups; Temperley lieb algebras; Strings in an expanded universe; and Chiral splitting and unitarity of closed superstrings. 
A Pasquier algebra is a commutative associative algebra of normal matrices attached to a graph. I review various appearances of such algebras in different contexts: operator product algebras and
Conformal, integrable and topological theories, graphs and Coxeter groups
I review three different problems occuring in two dimensional field theory: 1) classification of conformal field theories; 2) construction of lattice integrable realizations of the latter; 3)
On quantum symmetries of the non–ADE graph F4
We describe quantum symmetries associated with the F4 Dynkin diagram. Our study stems from an analysis of the (Ocneanu) modular splitting equation applied to a partition function which is invariant
Conformal Boundary Conditions
The question of boundary conditions in conformal field theories is discussed, in the light of recent progress. Solving the consistency condition known as Cardy equation is shown to amount to the
C-algebras and their applications to reflection groups and conformal field theories
The aim of this lecture is to present the concept of C-algebra and to illustrate its applications in two contexts: the study of reflection groups and their folding on the one hand, the structure of