Role of space-time foam in breaking supersymmetry via the Barbero-Immirzi parameter

We discuss how: (i) a dilaton/axion superfield can play the role of a Barbero-Immirzi field in four-dimensional conformal quantum supergravity theories, (ii) a fermionic component of such a dilaton/axion superfield may play the role of a Goldstino in the low-energy effective action obtained from a superstring theory with $F$-type global supersymmetry breaking, (iii) this global supersymmetry breaking is communicated to the gravitational sector via the supergravity coupling of the Goldstino, and (iv) such a scenario may be realized explicitly in a D-foam model with D-particle defects fluctuating stochastically.

Figure 1

(a) Schematic representation of a generic D-particle space-time foam model, in which matter particles are treated as open strings propagating on a D3-brane, and the higher-dimensional bulk space-time is punctured by D-particle defects. Consistent supersymmetric D-particle foam models can be constructed. No recoil and no brane motion yields zero vacuum energy and unbroken supersymmetry. Recoil contributions to vacuum energy yield broken supersymmetry. (b) Details of the process whereby an open string state propagating on the D3-brane is captured by a D-particle defect, which then recoils. This process involves an intermediate composite state that persists for a period $\delta t\sim {\alpha }^{\prime }E$, where $E$ is the energy of the incident string state. This distorts the surrounding space-time during the scattering process, leading to an effective refractive index, but not birefringence. Components of the recoil velocity perpendicular to the D3-brane world lead to vacuum energy contributions and thus target-space supersymmetry breaking.

Figure 2

The one-loop effective potential for the linearizing field $\rho (x)$ in the effective action (83), which is suitable for dynamical breaking of local supersymmetry and the generation of a gravitino mass. For certain values of the relevant parameters the potential has a minimum at zero, indicating an effective vanishing cosmological constant.