MA5P8 - CONFORMAL FIELD THEORY - Section 3

Section 3
Free bosonic CFTs


With the techniques introduced for free fermion theories in Section 2, it is now easy to carry out a similar analysis for free bosonic theories. They, too, allow a Fock space representations, but while for the free fermions these only produce three distinct lowest weight representations of the Virasoro algebra at c=1/2, we now find infinitely many such representations of the Virasoro algebra with c=1. I discuss the characters of these Fock space representations, reducibility, and modular invariant partition functions. For the latter, I also sketch a derivation using a semiclassical approach, which allows us to interpret them in terms of a free boson compactified on a circle.