Effective spin-two particles

7.5 Effective spin-two particles

Related to the previous point is the possibility of having quantum systems with no pre-geometric notions whatsoever (i.e., a condensed-matter–like system) that still exhibit in their low-energy spectrum effective massless spin-two excitations. This precise question has been investigated in [262 , 263 , 693 , 694

] for abstract quantum systems based on the underlying notion of qubits. Although not fully conclusive, these works indicate the possible existence of systems exhibiting purely helicity $±2$ excitations. One crucial ingredient in these constructions is the existence of a specific vacuum state with the characteristics of a string-net condensate.

These authors also show that it is not easy to have just helicity $±2$ excitations – typically one would also generate helicity $±1$ and massless scalar excitations. This is what would happen, for instance, in the emergent gravity scenario inspired in the phenomenology of ³He, which will be described below.