D3-brane model building and the supertrace rule

Overview & Synopsis

A common way to obtain Standard-Model-like Lagrangians in String Theory is to place D3 branes inside flux compactifications. The bosonic and fermionic masses and couplings of the resulting gauge theory are determined by the ten-dimensional metric and the fluxes respectively, and the breaking of supersymmetry is soft. However, not any soft-supersymmetry-breaking Lagrangian can be obtained this way, since the String Theory equations of motion impose certain relations between the soft couplings. We show that these relations imply that the sums of the squares of the boson and of the fermion masses are equal and that, furthermore, one- and two-loop quantum corrections do not spoil this equality. This makes problematic the use of D3 branes for constructing models for physics beyond the Standard Model.