A Heterotic Hermitian--Yang--Mills Equivalence

Abstract

We consider N=1, d=4 vacua of heterotic theories in the large radius limit in which alpha' << 1. We construct a real differential operator $\mathcal{D}=D+\bar{D}$ on an extension bundle $(Q,\mathcal{D})$ with underlying topology $Q=(T^{1,0}X{)}^{\ast }\oplus \mathrm{End}E\oplus T^{1,0}X$ whose curvature is holomorphic and Hermitian-Yang-Mills with respect to the complex structure and metric on the underlying non-Kahler complex 3-fold X if and only if the heterotic supersymmetry equations and Bianchi identity are satisfied. This is suggestive of an analogue of the Donaldson--Uhlenbeck--Yau correspondence for heterotic vacua of this type.

34 pages; v2 references updated, typos fixed