Angle Defect for Super Triangles

Robert Penner ()
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Robert Penner: Institut des Hautes Études Scientifiques, Le Bois Marie

Chapter Chapter 6 in Essays on Geometry, 2025, pp 81-109 from Springer

Abstract: 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.

Date: 2025
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DOI: 10.1007/978-3-031-76257-4_6

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