D3-Brane Model Building and the Supertrace Rule.

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 for D3-branes in background fluxes, 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 the use of D3-branes for constructing computationally controllable models for physics beyond the standard model problematic.