We examine to what extent heterotic string worldsheets can describe
arbitrary $E_8 × E_8$ gauge fields. The traditional construction of heterotic
strings builds each $E_8$ via a $Spin(16)/Z2$ subgroup, typically realized
as a current algebra by left-moving fermions, and as a result, only $E_8$
gauge fields reducible to $Spin(16)/Z_2$ gauge fields are directly realizable
in standard constructions. However, there exist perturbatively consistent
$E_8$ gauge fields which cannot be reduced to $Spin(16)/Z_2$ and so
cannot be described within standard heterotic worldsheet constructions.
A natural question to then ask is whether there exists any $(0,2)$ superconformal
field theory (SCFT) that can describe such $E_8$ gauge fields. To
answer this question, we first show how each 10-dimensional $E_8$ partition
function can be built up using other subgroups than $Spin(16)/Z_2$, then
construct “fibered WZW models” which allow us to explicitly couple current
algebras for general groups and general levels to heterotic strings.
This technology gives us a very general approach to handling heterotic
compactifications with arbitrary principal bundles. It also gives us a
physical realization of some elliptic genera constructed recently by Ando
and Liu.