Non-perturbative heterotic duals of M-theory on G₂ orbifolds

Abstract

By fibering the duality between the E₈ × E₈ heterotic string on T³ and M-theory on K3, we study heterotic duals of M-theory compactified on G₂ orbifolds of the form T⁷/${\mathbb{Z}}_2^3$. While the heterotic compactification space is straightforward, the description of the gauge bundle is subtle, involving the physics of point-like instantons on orbifold singularities. By comparing the gauge groups of the dual theories, we deduce behavior of a “half-G₂” limit, which is the M-theory analog of the stable degeneration limit of F-theory. The heterotic backgrounds exhibit point-like instantons that are localized on pairs of orbifold loci, similar to the “gauge-locking” phenomenon seen in Hořava-Witten compactifications. In this way, the geometry of the G₂ orbifold is translated to bundle data in the heterotic background. While the instanton configuration looks surprising from the perspective of the E₈ × E₈ heterotic string, it may be understood as T-dual Spin(32)/ℤ₂ instantons along with winding shifts originating in a dual Type I compactification.