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.
"Heterotic compactifications with principal bundles for general groups and general levels." Adv. Theor. Math. Phys. 14 (2) 335 - 397, April 20.