Three Generations of SM Gauge Symmetry from Non-SUSY Compactification on CP2 × S2

This paper investigates the dynamics of D-branes and tachyon condensation in non-supersymmetric string theory, focusing on how these processes realize Standard Model (SM) gauge symmetries. We discuss the distance-dependent potentials arising from D-brane separation and their implications for the Coleman-Weinberg potential. When D-branes coincide, an attractive force emerges due to massless states, reflecting symmetry-breaking phenomena. Tachyon condensation modifies the particle spectrum, providing masses to gauge bosons and fermions through interactions reminiscent of the Higgs mechanism. We show that the gauge symmetries are tied to the isometries of compactified spaces, with masses determined by the compactification scale. Our results indicate that nonsupersymmetric string theory can yield a viable realization of the SM, illuminating the relationship between brane dynamics, tachyon behavior, and mass generation.