Beltrami Flows & Holography = Holomorphy Hypothesis

Abstract

The field equations of TGD reduce to conservation laws for isometry charges so that TGD is analogous to hydrodynamics. Beltrami flows are indeed a basic aspect of TGD and it is interesting to relate them to the new visions of TGD, in particular the holography = holomorphy principle. The outcome of these considerations is that integrable flows, having interpretation as irrotational and incompressible Beltrami flows, have in TGD an interpretation as generalized complex flows reducing to gradient flows except at singularities. These flows definable for the generalized complex structure of H=M⁴ x CP₂ and X⁴ ⊂ H have a natural identification as hydrodynamical flows in the induced K"ahler field. These flows have as singularities are 2-D partonic surfaces and string world sheets. In the view of scattering amplitudes, vertices correspond to partonic 2-surfaces at which the lines of the analogs of Feynman diagrams meet each other whereas string world sheets as intersections of two 4-surfaces with common Hamilton-Jacobi structure characterize interactions as contact interactions.