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.
Highlights
Is compactified on a Calabi-Yau threefold equipped with a supersymmetric three-torus fibration
By fibering the duality between the E8 × E8 heterotic string on T 3 and Mtheory on K3, we study heterotic duals of M-theory compactified on G2 orbifolds of the form T 7/Z32
To understand the gauge symmetry and particle spectrum seen in our M-theory orbifold backgrounds, it is informative to look at another chain of dualities that relates M-theory to the Spin(32)/Z2 heterotic string
Summary
To obtain dual low energy effective theories in 4D, we will make use of the duality between the 7D theories arising from the E8 × E8 heterotic string on T 3 and M-theory on the compact 4-manifold known as a K3 surface [2] Evidence for this duality comes in part from the fact that these two compactifications share the same moduli space:. From the view of M-theory, the special points in the moduli space are orbifold limits of K3 that contain ADE singularities [2] That these singularities give rise to effective nonabelian gauge symmetry can be seen by blowing up an A1 singularity to give an exceptional P1: this cycle is dual to a harmonic 2-form, which gives an effective U(1) gauge field upon Kaluza-Klein reduction of the C-field.
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