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.