1105.5006

The title of this post refers to the pre-print of my paper which appeared in arxiv.org today. It's about domain wall formation in spontaneous R-parity breaking models and one possible way to get rid of them by introducing gravity induced higher dimensional operators. Before I go one step further may be I should say something about various technical terms appearing in the last sentence. Domain walls are two dimensional objects which are formed whenever a discrete symmetry gets spontaneously broken. They have a finite topological charge and hence are stable. In our work, this discrete symmetry is the left-right symmetry under which the left handed chiral fields are exchanged with right handed chiral fields and vice versa. Left(right) handed means direction of spin is opposite(same) to (as) the direction of momentum. This discrete symmetry arises in one very promising extension of standard model of particle physics where tiny neutrino masses naturally arise by seesaw mechanism. These domain walls are extended objects and hence will start dominating the Universe after the matter and radiation energy density decreases below a certain limit. However this is against observation, as we know our Universe is mostly matter dominated (+ a cosmological constant) from WMAP and other related experiments. Thus there needs to be some mechanism to make these walls disappear. One possible idea is to create a small pressure difference between two sides of the wall so that the true vacuum expands to occupy the entire causal Universe. We have talked about gravity induced higher dimensional terms (> dimension 4) which break the discrete symmetry explicitly creating the required pressure difference. How these higher dimensional terms break parity is a part of some higher theory (may be hidden sector supersymmetry breaking models, or some quantum gravity models) and we do not discuss that further in our paper. The domain wall disappearance through this mechanism however puts strict constraints on the discrete symmetry breaking scale. In one class of models (having Higgs triplets and hence type II seesaw), this symmetry breaking scale has to be pretty low (< 10^5 - 10^7 GeV) . But if this theory is a part of some higher theory such as SO(10) grand unified theory, then this left-right symmetry breaking scale has to be pretty high and hence is in disagreement with the constraints coming from domain wall removal. We also discuss another class of models (with Higgs doublets and hence type III or inverse seesaw) where both these constraints can be satisfied simultaneously. The good thing about models with Higgs doublets is that domain wall removal does not put very strict constraints on the symmetry breaking scales and hence do not give rise to conflict with grand unification which usually forces the symmetry breaking scale to be very high. Comments and criticism are welcome :)