engleski

Some applications and constructions of intertwining operators in Logarithmic Conformal Field Theory

We discuss some applications of fusion rules and intertwining operators in the representation theory of orbifolds of triplet vertex algebras. We prove that the classification of irreducible modules for vertex algebra $W(p) ^{; ; ; ; A_m}; ; ; ; $ follows from (conjectural) fusion rules from singlet vertex algebra. In the case of $p=2$ we rigorously prove fusion rules formulas in the framework of vertex algebras and intertwining operators, so our result gives a classification of modules for $W(p)^{; ; ; ; A_m}; ; ; ; $ for $p=2$. We also present a new deformed realization of triplet and singlet vertex algebras which gives a construction of certain intertwining operators which cannot be detected using standard free field realization.

triplet vertex algebra ; singlet vertex algebras ; fusion rules ; intertwining operators

ISBN: 978-1-4704-2666-8 (print)