Heterotic compactifications with principal bundles for general groups and general levels

TL;DR

The paper addresses whether perturbative heterotic strings can realize all $E_8\times E_8$ gauge fields, highlighting that standard constructions restricted to $Spin(16)/\mathbb{Z}_2$-reducible bundles miss a class of exotic $E_8$ bundles. It develops fibered WZW models to couple general current algebras at level $k$ to heterotic strings, enabling arbitrary principal bundles and nontrivial levels, and derives a generalized anomaly cancellation condition $k\,\mathrm{Tr}F^2 = \mathrm{Tr}R^2$. The authors illustrate explicit examples using $(SU(5)\times SU(5))/\mathbb{Z}_5$ on K3, discuss F-theory duals, and connect the construction to elliptic genera studied in mathematics, revealing new perturbative CFTs for heterotic strings. These results broaden the landscape of viable heterotic vacua and provide tools for realizing gauge sectors beyond traditional worldsheet realizations, with potential implications for string phenomenology and duality studies.

Abstract

We examine to what extent heterotic string worldsheets can describe arbitrary E8xE8 gauge fields. The traditional construction of heterotic strings builds each E8 via a Spin(16)/Z2 subgroup, typically realized as a current algebra by left-moving fermions, and as a result, only E8 gauge fields reducible to Spin(16)/Z2 gauge fields are directly realizable in standard constructions. However, there exist perturbatively consistent E8 gauge fields which can not be reduced to Spin(16)/Z2, and so cannot be described within standard heterotic worldsheet constructions. A natural question to then ask is whether there exists any (0,2) SCFT that can describe such E8 gauge fields. To answer this question, we first show how each ten-dimensional E8 partition function can be built up using other subgroups than Spin(16)/Z2, 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.