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A Heterotic Hermitian--Yang--Mills Equivalence
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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 $Q=(T^{1,0}X)^* \oplus {\rm End} \, E \oplus T^{1,0} X$ 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.
Forward citations
Cited by 3 Pith papers
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Heterotic moduli, the double extension and the alpha'^2 metric
The heterotic moduli-space metric picks up a torsion-induced complex-structure–hermitian mixing term at order α'^2, while the Kähler potential keeps its functional form.
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Stringy Corrections to Heterotic SU(3)-Geometry
At second order in alpha', heterotic SU(3) compactifications with a smooth large-radius limit obey the same complex geometric equations as Strominger's first-order system, and the Hull connection is not an instanton.
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Universal geometry as an organising principle for heterotic moduli
Universal geometry is shown to be consistent with the alpha'^2-corrected heterotic supersymmetry equations when the composite Hull connection is used as the universal tangent-bundle connection.
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