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We examine to what extent heterotic string worldsheets can describe arbitraryE8xE8 gauge fields. The traditional construction of heterotic strings buildseach E8 via a Spin(16)/Z2 subgroup, typically realized as a current algebra byleft-moving fermions, and as a result, only E8 gauge fields reducible toSpin(16)/Z2 gauge fields are directly realizable in standard constructions.However, there exist perturbatively consistent E8 gauge fields which can not bereduced to Spin(16)/Z2, and so cannot be described within standard heteroticworldsheet constructions. A natural question to then ask is whether thereexists any (0,2) SCFT that can describe such E8 gauge fields. To answer thisquestion, we first show how each ten-dimensional E8 partition function can bebuilt up using other subgroups than Spin(16)/Z2, then construct ``fibered WZWmodels'' which allow us to explicitly couple current algebras for generalgroups and general levels to heterotic strings. This technology gives us a verygeneral approach to handling heterotic compactifications with arbitraryprincipal bundles. It also gives us a physical realization of some ellipticgenera constructed recently by Ando and Liu.Comment: 48 pages, LaTeX; v2: references added; v3: typos fixe

Heterotic compactifications with principal bundles for general groups and general levels