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Angle Defect for Super Triangles

In: Essays on Geometry

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  • Robert Penner

    (Institut des Hautes Études Scientifiques, Le Bois Marie)

Abstract

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 N = 1 $${\mathcal N}=1$$ super hyperbolic geometry and provides a novel non-trivial additive function of super triangles. The proof techniques involve the orthosymplectic group OSp ( 1 | 2 ) $$\mathrm {OSp}(1|2)$$ in its action on the super Minkowski space ℝ 2 , 1 | 2 $${\mathbb R}^{2,1|2}$$ and brute-force computation.

Suggested Citation

  • Robert Penner, 2025. "Angle Defect for Super Triangles," Springer Books, in: A. Muhammed Uludağ & Ayberk Zeytin (ed.), Essays on Geometry, chapter 0, pages 81-109, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-76257-4_6
    DOI: 10.1007/978-3-031-76257-4_6
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