A novel solution to the gravitino problem

Abstract

Abstract 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 ($$ \overline{\textrm{D}3} $$ D 3 ¯ -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., X2 = 0) which is present only inside the $$ \overline{\textrm{D}3} $$ D 3 ¯ -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 Λ, the supersymmetry breaking $$ \overline{\textrm{D}3} $$ D 3 ¯ -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., $$ {\hat{m}}_{3/2} $$ m ̂ 3 / 2 > 100 GeV) due to the supersymmetry breaking tension of the $$ \overline{\textrm{D}3} $$ D 3 ¯ -branes. Here, the super-particles can be heavy enough to have avoided detection so far. Since the open string Goldstino exists only inside the $$ \overline{\textrm{D}3} $$ D 3 ¯ -branes, the gravitino is heavy only inside the $$ \overline{\textrm{D}3} $$ D 3 ¯ -branes, but massless or ultra-light outside the $$ \overline{\textrm{D}3} $$ D 3 ¯ -branes. This means that the gravitinos will be pushed out of the $$ \overline{\textrm{D}3} $$ D 3 ¯ -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 Λobs.