I had the experience of reading TGD vision about early phase of Universe! The strong feeling was that the scientists had forgotten to mention that the idea came from my homepage and perhaps from the articles published in Prespacetime Journal edited by Huping Hu. This has happened so many times during years.
Of course, I might be oversensitivized by this kind of sad experiences during years. So many key ideas of TGD have been "independently discovered" in watered down and hopelessly poorly understood form during years. It is very difficult to move a plant from TGD Universe to say string model Universe without killing it. I of course hope that I am wrong. Perhaps the authors indeed invented it themselves. But it is so difficult to believe that professional scientists could be blind enough to avoid learning about the existence of TGD during IT era. If so, they do not deserve to be called scientists.
What is the message of the authors.
- The authors do not talk about flux tubes in TGD sense (as 3-D surfaces, here string theorist could talk about 3-D branes) but in the sense of gauge theories in D-dimensional space-time. The proposal is that the network of tightly knotted linked flux tubes is topologically stable only in space-time dimension D=4.
- Dimension d=3 is indeed unique as space dimension and D=4 as space-time dimension. The point is that n-dimensional objects are knotted in dimension n+2 and linked in dimension 2n+1. d= 3 = 1+2=2×1+1 allows both knotting and linking of 1-D objects simultaneously, and is therefore a unique dimension of space. Even more, in space-time dimension D=4 the 2-D orbits of knots form 2-knots which add still more topological complexity to D=4 and makes it unique.
- These flux tubes - cosmic strings - are 3-D surfaces in M4×CP2 with 2-D minimal surface (string world sheet) as M4 projection and 2-D complex surface of CP2 as CP2 projection. During the primordial period one had gas or plasma of cosmic strings.
- After the primordial period the 4-D space-time in the sense of GRT began to emerge as space-time regions with 4-D M4 projection. The M4 projection of flux tubes became 4-D instead of 2-D and began to thicken in spatial directions. Flux tubes topologically condensed at thicker flux tubes (glued by tiny wormhole contacts to larger 3-surfaces). As approximately 1-D objects they could form knots and get linked. Their approximately 2-D orbits could also get knotted and these 2-knots are something completely new. This transition is the TGD analog of inflationary period and solves its grave problems.
- Knotting and linking are not actually approximation notions. Fermionic strings parallel to cosmic strings were present and served as topological representatives for the flux tubes. They knotted and linked in 3-D sense and 2-knotted in 4-D sense.
- Cosmic strings as flux tubes carrying magnetic monopole flux are fundamental for the entire TGD Universe and appear in all length scales. Flux tubes are also fundamental in TGD variant of hadronic physics, nuclear physics, molecular physics, quantum biology, etc...
- Generalization of conformal invariance is possible for 3-D light-like surfaces since their metric dimension is D=2. Boundary of light-cone in 4-D Minkowski space has this generalized conformal invariance. Also the 3-D light-like surfaces between Euclidian and Minkowskian regions have this symmetry. This gives rise to the huge conformal symmetries extending stringy conformal symmetries implying among other things strong form of holography in which locally 2-D data determined 4-D space-time surfaces and quantum states.
A kind of record in professional arrogance is that I have been preaching about this simple but overall important observation for almost three decades and in vain! Colleagues simply refuse to listen! They read only prestigious journals as one my finnish colleagues formulated it! Collective stupidity is one of the most irritating and fascinating sociological phenomena.
- In number theoretical vision about TGD associativity condition of space-time as surfaces in 8-D space with octonionic structure forces D=4. Associativity holds for space-time surfaces assignable to external particles. Not for interaction regions and this leads to a beautiful interpretation of dynamics (see this).
- The twistor lift of TGD by generalizing twistor structure to its 8-D variant and inducing 4-D twistpr structure is possible only for this space-time dimension. Induced twistors are essentially 4-D notion. Also this makes sense only 4-D space-time surfaces in 8-D imbedding space M4×CP2 (see this and this).