### A connection of singularities of minimal surfaces with generation of Higgs vacuum expectation?

String world sheet appear as singularities of space-time surfaces as minimal surfaces. At string world sheets minimal surface equations fail and there is transfer of Noether charges associated with Kähler and volume degrees of freedom at string world. This has interpretation as analog for the interaction of charged particle with Maxwell field.

What about the physical interpretation of the singular divergences of the isometry currents J_{A} of the volume action located at string world sheet?

- The divergences of J
_{A}are proportional to the trace of the second fundamental form H formed by the covariant derivatives of gradients ∂_{α}h^{k}of H-coordinates in the interior and vanish. The singular contribution at string world sheets is determined by the discontinuity of the isometry current J_{A}and involves only the first derivatives ∂_{α}h^{k}.

- One of the first questions after ending up with TGD for 41 years ago was whether the trace of H in the case of CP
_{2}coordinates could serve as something analogous to Higgs vacuum expectation value. The length squared for the trace has dimensions of mass squared. The discontinuity of the isometry currents for SU(3) parts in h=u(2) and its complement t, whose complex coordinates define u(2) doublet. u(2) is in correspondence with electroweak algebra and t with complex Higgs doublet. Could an interpretation as Higgs or even its vacuum expectation make sense?

- p-Adic thermodynamics explains fermion masses elegantly (understanding of boson masses is not in so good shape) in terms of thermal mixing with excitations having CP
_{2}mass scale and assignable to short string associated with wormhole contacts. There is also a contribution from long strings connecting wormhole contacts and this could be important for the understanding of weak gauge boson masses. Could the discontinuity of isometry currents determine this contribution to mass. Edges/folds would carry mass.

- The non-singular part of the divergence multiplying 2-D delta function has dimension 1/length squared and the square of this vector in CP
_{2}metric has dimension of mass squared. Could the interpretation of the discontinuity as Higgs expectation make sense? If so, Higgs expectation would vanish in the space-time interior.

Could the interior modes of the induced spinor field - or at least the interior mode of right-handed neutrino ν

_{R}having no couplings to weak or color fields - be massless in 8-D or even 4-D sense? Could ν_{R}and νbar_{R}generate an unbroken*N*=2 SUSY in interior whereas inside string world sheets right-handed neutrino and antineutrino would be eaten in neutrino massivation and the generators of*N*=2 SUSY would be lost somewhat like charged components of Higgs!

If so, particle physicists would be trying to find SUSY from wrong place. Space-time interior would be the correct place. Would the search of SUSY be condensed matter physics rather than particle physics?

For a summary of earlier postings see Latest progress in TGD.