Top Quark Mass from D-Brane Intersection Angles

A geometric derivation of the top quark mass is presented within a D-brane compactification framework, in which fermion masses arise from trigonometric overlap factors determined by intersection angles. The top quark mass is shown to follow from the relation mt = v sin (πNc/k), where v = 246 GeV is the electroweak scale, Nc = 3 is the number of colors, and k = 12 is the orbifold order. This yields mt = v sin (π/4) ≈ 174 GeV, in agreement with the experimentally measured value to within 0.8%. Scalar sector details and vacuum energy constraints are addressed in prior work.