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<p>We prove, under suitable global assumptions, that the only heterotic horizons with closed 3-form field strength that preserve strictly 6 supersymmetries have spatial horizon section diffeomorphic either to <i>SU</i> (3) or to <i>S</i><sup>2</sup> × <i>S</i><sup>3</sup> × <i>SO</i>(3), up to identifications with the action of a discrete group. Under similar assumptions, which include the compactness of the transverse space, we demonstrate that there are no heterotic AdS<sub>3</sub> solutions that preserve 6 supersymmetries. The proof is based on a topological argument.</p><p>We also re-examine the conditions required for the existence of such backgrounds that preserve 4 supersymmetries focusing on those that admit an additional <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <msup> <mo>⊕</mo> <mn>2</mn> </msup> <mi mathvariant="bold-fraktur">u</mi> <mfenced close=")" open="("> <mn>1</mn> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( {\oplus}^2\mathbf{\mathfrak{u}}(1) \)</EquationSource> </InlineEquation> symmetry. We provide some additional explanation for the existence of solutions and point out the similarities that these conditions have with those that have recently emerged in the classification of compact strong 6-dimensional Calabi-Yau manifolds with torsion.</p>

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Heterotic horizons and AdS3 backgrounds that preserve 6 supersymmetries

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  • 发表日期：

    2026年7月9日

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  • Georgios Papadopoulos

摘要

We prove, under suitable global assumptions, that the only heterotic horizons with closed 3-form field strength that preserve strictly 6 supersymmetries have spatial horizon section diffeomorphic either to SU (3) or to S2 × S3 × SO(3), up to identifications with the action of a discrete group. Under similar assumptions, which include the compactness of the transverse space, we demonstrate that there are no heterotic AdS3 solutions that preserve 6 supersymmetries. The proof is based on a topological argument.

We also re-examine the conditions required for the existence of such backgrounds that preserve 4 supersymmetries focusing on those that admit an additional ⊕ 2 u 1 \( {\oplus}^2\mathbf{\mathfrak{u}}(1) \) symmetry. We provide some additional explanation for the existence of solutions and point out the similarities that these conditions have with those that have recently emerged in the classification of compact strong 6-dimensional Calabi-Yau manifolds with torsion.