The concrete model for elementary particles has developed gradually during years and is by no means final. In the recent model elementary particle corresponds to a pair of wormhole contacts and monopole flux runs between the throats of of the two contacts at the two space-time sheets and through the contacts between space-time sheets.
The first criticism relates to twistor lift of TGD. In the case of Kähler action the wormhole contacts correspond to deformations for pieces of CP2 type vacuum extremals for which the 1-D M4 projection is light-like random curve. Twistor lift adds to Kähler action a volume term proportional to cosmological constant and forces the vacuum extremal to be a minimal surface carrying non-vanishing light-like momentum (this is of course very natural): one could call this surface CP2 extremal. This implies that M4 projection is light-like geodesic: this is physically rather natural.
Twistor lift leads to a loss of the proposed space-time correlate of massivation used also to justify p-adic thermodynamics: the average velocity for a light-like random curve is smaller than maximal signal velocity – this would be a clear classical signal for massivation. One could however conjecture that the M4 projection for the light-like boundaries of string world sheets becomes light-like geodesic of M4× CP2 instead light-like geodesic of M4 and that this serves as the correlate for the massivation in 4-D sense.
Second criticism is that I have not considered in detail what the monopole flux hypothesis really means at the level of detail. Since the monopole flux is due to the CP2 topology, there must be a closed 2-surface which carries this flux. This implies that the flux tube cannot have boundaries at larger space-time surface but one has just the flux tube which closed cross section obtained as a deformation of a cosmic string like object X2× Y2, where X2 is minimal surface in M4 and Y2 a complex surface of CP2 characterized by genus. Deformation would have 4-D M4 projection instead of 2-D string world sheet.
Note: One can also consider objects for which the flux is not monopole flux: in this case one would have deformations of surfaces of type X2× S2, S2 homologically trivial geodesic sphere: these are non-vacuum extremals for the twistor lift of Kähler action (volume term). The net magnetic flux would vanish – as a matter fact, the induced Kähler form would vanish identically for the simplest situation. These objects might serve as correlates for gravitons since the induced metric is the only field degree of freedom. One could also have non-vanishing fluxes for flux tubes with disk-like cross section.
If this is the case, the elementary particles would be much simpler than I have though hitherto.
For a summary of earlier postings see Latest progress in TGD.