Technique in computing the characters of VOA modules using vector-valued functions for modular groups
Keywords:
vector-valued functions, vertex operator algebra(VOA), Modular tensor category(MTC)Abstract
For a rational vertex operator algebra (VOA) with a
-graded simple
-module
, there is a corresponding character
where is the subspace of
on which
acts by multiplication by
,
is the central charge of
and
.
In this paper, we apply the notion of vector-valued functions for a modular group from the work of Peter Bantay and Terry Gannon to compute the -module character
. With the relation among simple
-modules
and their corresponding simple objects of modular tensor category (MTC)
, we can use the central charge and conformal weights of the MTC
to compute the character
. This technique can be used to compute
up to central charge
by the restriction mentioned in P. Bantay paper.
