Angle Defect for Super Triangles

Abstract

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