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