D3-brane model building and the supertrace rule

TL;DR

This paper investigates the mass relations in D3-brane models within flux compactifications, revealing that supersymmetry-breaking soft terms satisfy specific sum rules that are preserved quantum mechanically, impacting model building.

Contribution

It demonstrates that D3-brane models impose a supertrace mass relation due to string theory constraints, affecting their viability for realistic model construction.

Findings

Mass sums of bosons and fermions are equal in these models.

Quantum corrections do not violate the supertrace relation.

String theory equations of motion restrict soft supersymmetry-breaking terms.

Abstract

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.