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We prove that the angle defect minus the area of a super hyperbolic triangle is not identically zero and explicitly compute the non-vanishing fermionic correction. This disproves the Angle Defect Theorem for \({\mathcal N}=1\) super hyperbolic geometry and provides a novel non-trivial additive function of super triangles. The proof techniques involve the orthosymplectic group \(\mathrm {OSp}(1|2)\) in its action on the super Minkowski space \({\mathbb R}^{2,1|2}\) and brute-force computation.

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Angle Defect for Super Triangles

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  • 发表日期：

    2025年

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  • Robert Penner

摘要

We prove that the angle defect minus the area of a super hyperbolic triangle is not identically zero and explicitly compute the non-vanishing fermionic correction. This disproves the Angle Defect Theorem for \({\mathcal N}=1\) super hyperbolic geometry and provides a novel non-trivial additive function of super triangles. The proof techniques involve the orthosymplectic group \(\mathrm {OSp}(1|2)\) in its action on the super Minkowski space \({\mathbb R}^{2,1|2}\) and brute-force computation.