A Heterotic Hermitian--Yang--Mills Equivalence

We consider N = 1, d = 4 vacua of heterotic theories in the large radius limit in which α << 1. We construct a real differential operator D = D + D¯ on an extension bundle (Q, D) with underlying topology Q = (T^1,0X)^∗ ⊕ End E ⊕ T^1,0X whose curvature is holomorphic and Hermitian–Yang–Mills with respect to the complex structure and metric on the underlying non-Kähler 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.