Fractons and TGDIn Quanta Magazine there was a highly interesting article about entities known as fractons (see this). There seems to be two different views about fractons as one learns by going to Wikipedia. Fracton can be regarded as a as selfsimilar particlelike entity (see this or as "subdimensional" particle unable to move in isolation (see this). I do not understand the motivation for "subdimensional". It is also unclear whether the two notions are related. The popular article assigns to the fractons both the fractal character and the inability to move in isolation. The basic idea is however that discrete translational symmetry is replaced with a discrete scaling invariance. The analog of lattice which is invariant under discrete translations is fractal invariant under discrete scalings. One can also consider the possibility that the time evolution operator would act as scaling rather than translation. This is something totally new from quantum field theory (QFT) point of view. In QFTs energy corresponds to time translational symmetry and Hamiltonian generates infinitesimal translations. In string models the analog of stringy Hamiltonian is the infinitesimal scaling operator, Virasoro generator L_{0}. In TGD the extension of physics to adelic physics provides number theoretic and geometric descriptions as dual descriptions of physics (see for instance this, this, and this). This approach also provides insights about fractons as scale invariant entities and.
In TGD number theoretical vision leads to the notion of Galois confinement analogous to color confinement. The Galois group of a given extension of rationals indeed acts as a symmetry at spacetime level. In TGD inspired biology Galois groups would play a fundamental role. For instance, dark analogs of genetic codons, codon pairs, and genes would be singlets (invariant) under an appropriate Galois group and therefore behave as a single quantum coherent dynamical and informational unit. See (see this and this) . Suppose that one has a system  say a fractal analog of a lattice consisting of Galois singlets. Could fracton be identified as a state which is analogous to quark or gluon and therefore not invariant under the Galois group. The physical states could be formed from these as Galois singlets and are like hadrons. See the chapter Quantum Criticality and Dark Matter: part II.
