17 - The space of string vacua

Summary

In the preceding chapters we have displayed the wealth of possibilities to build specific 4d string vacua. In this chapter we take a more general viewpoint and present an aerial view of the space of string vacua (at our present level of knowledge), in particular of those corners with low-energy physics resembling closely the SM of particle physics. In spite of the apparent enormous number of consistent vacua, the space of field theories obtainable as low-energy effective descriptions of string theories can be argued to be strongly constrained, forming a minute subset in the space of all possible field theories. We present some of these general properties of string vacua, and then turn to overviewing the status of realistic vacua searches in different string compactification setups. These explicit models are presumably only the tip of the iceberg in the set of semi-realistic models in string theory, which we term the flavour landscape. In addition, the latter may be complemented by additional ingredients like flux degrees of freedom, yielding a large multiplicity of vacua, known as the flux landscape. Our outlook summarizes some general reflections on string theory and particle physics, inspired by this general perspective.

General properties of the massless spectrum in string compactifications

The spectrum and symmetries of light particles in 4d string compactifications is very model dependent. There are, however, several important general properties valid in any compactification, and which can provide non-trivial constraints in model building.