- The conformal structures of partonic 2-surfaces are classified by their conformal moduli expressible in terms of Teichmueller parameters (see this). Could one consider some kind of analytical continuation of the moduli spaces of the partonic 2-surfaces with different topologies to moduli spaces of time-like string world sheets?
This would give a direct connection with p-adic mass calculations in which the (p-adic counterparts of) these moduli spaces are central. In p-adic mass calculations (see this and this), one assumes only partonic 2-surfaces. However, the recent proposal for the construction of preferred extremals of action as minimal surfaces, realizing holography in terms of a 4-D generalization of the holomorphy of string world sheets and partonic 2-surfaces, assumes a 4-D generalization of 2-D complex structure and this generalization could be just Hamilton-Jacobi structure.
- The boundaries of a string world sheet can also have space-like portions and they would be analogous to the punctures of 2-D Euclidian strings (now partonic 2-surfaces are closed).
- Can Minkowskian string world sheets have handles? What would the handle of a string world sheet look like? String world sheets have ends at the boundaries of the causal diamond (CD) playing a central role in zero energy ontology (ZEO).
If the 1-D throat of the handle is a smooth curve, it must have portions with both space-like and time-like normal: this is possible in the induced metric but the portion with a time-like normal should carry vanishing conserved currents. For area action this is not possible. Intuitively, the throat of the handle would look physically to a splitting of a planar string to two pieces such that the conserved currents go to the handle. If this is the case, the 1-D throat would have two corners at which two time-like halves of the throat meet.
The handle would be obtained by moving the throat along a space-like curve such that its Minkowskian signature and singularity are preserved. CP2 contribution to the induced metric might make this possible.
For a summary of earlier postings see Latest progress in TGD.
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.