A novel solution to the gravitino problem

In a general phenomenological model with local supersymmetry, the amount of massive gravitinos produced in early universe tends to violate the known dark matter density bound by many orders of magnitude. In the brane world scenario in Type IIB string theory, we propose a novel way to evade this problem. There, the standard model of strong and electroweak interactions live inside the anti-D3-branes (<(D3)over bar >-branes) that span the 3 large spatial dimensions. Here, the potential Goldstino to be absorbed by the gravitino (to become massive) is the fermion component of the open string nilpotent superfield X (i.e., X-2 = 0) which is present only inside the <(D3)over bar >-branes. This non-linear supergravity scenario offers 2 ways to solve the gravitino problem, with very different particle physics phenomenologies: (1) To satisfy the necessary condition for a naturally small cosmological constant lambda, the supersymmetry breaking <(D3)over bar >-branes tension is precisely cancelled by the Higgs spontaneous symmetry breaking effect, so the gravitino is ultra-light and its contribution to the dark matter density is negligible. If exist, the super-particles should have already been detected in experiments. To avoid contradiction with their non-observation, X is applied to project out all the R-parity odd fields. Consequently, this non-linear supergravity model is almost identical to the standard model. (2) As an alternative, one can have a massive gravitino (e.g., mb(3/2) > 100 GeV) due to the supersymmetry breaking tension of the <(D3)over bar >-branes. Here, the super-particles can be heavy enough to have avoided detection so far. Since the open string Goldstino exists only inside the <(D3)over bar >-branes, the gravitino is heavy only inside the <(D3)over bar >-branes, but massless or ultra-light outside the <(D3)over bar >-branes. This means that the gravitinos will be pushed out of the <(D3)over bar >-branes to the extra dimensions in the bulk, a phenomenon analogous to the Meissner effect for the massive photons inside super-conductors but massless outside. As a result, the massive gravitinos will be depleted so the gravitino problem is absent. In this case, a fine-tuning is necessary to obtain the very small observed lambda(obs).

Automated summary

In the brane world scenario of string theory, a novel solution to the excessive gravitino production problem in the early universe is proposed. By introducing a non-linear supergravity model with (anti-D3)-branes, different particle physics phenomenologies can be used to solve the problem and simultaneously explain the small observed cosmological constant.