Infinitesimal moduli of G2 holonomy manifolds with instanton bundles

Understand

We describe the infinitesimal moduli space of pairs $(Y, V)$ where $Y$ is a manifold with $G_2$ holonomy, and $V$ is a vector bundle on $Y$ with an instanton connection.

• These structures arise in connection to the moduli space of heterotic string compactifications on compact and non-compact seven dimensional spaces, e.g.
• domain walls.
• Employing the canonical $G_2$ cohomology developed by Reyes-Carri\'on and Fern\'andez and Ugarte, we show that the moduli space decomposes into the sum of the bundle moduli $H^1_{\check{d}_A}(Y,\mathrm{End}(V))$ plus the moduli of the $G_2$ structure preserving the instanton condition.