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Universality of the holomorphic solution ansatz and the notion of effective action

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The explicit solution of field equations in terms of the generalized holomorphy is now known. Also the emergence of supersymplectic symmetry is understood: it emerges as symmetries of Chern-Simons-Kähler action at the 3-D partonic orbits defining part of 3-D holographic data.

The solution ansatz is independent of action as long it is general coordinate invariance depending only on the induced geometric structures. Space-time surfaces would be minimal surfaces apart from lower-dimensional singular surfaces at which the field equations involve the entire action. Only the singularities, classical charges and positions of topological interaction vertices depend on the choice of the action (see this). Kähler action plus volume term is the choice of action forced by twistor lift making the choice of H unique.

The universality has a very intriguing implication. One can assign to any action of this kind conserved Noether currents and their fermionic counterparts (also super counterparts). One would have a huge algebra of conserved currents characterizing the space-time geometry. The corresponding charges need not be conserved since the conservation conditions at the partonic orbits and other singularities depend on the action. The discussion of the symplectic symmetries leads to the conclusion that they give rise to conserved charges at the partonic 3-surfaces obeying Chern-Simons-Kähler dynamics, which is non-deterministic.

Could the measurement of the conserved charges associated with a particular action project to states, which are superpositions of space-time surfaces involving only those partonic orbits for which they are conserved? Or does it make sense to speak of the measurement of action? Partonic 3-surfaces would be in the same role as space-like 3-surfaces as initial data: the time coordinate for this time evolution would be dual to the light-like coordinate of the partonic orbit. Could this relate to the notion of effective action used in quantum field theories as a characterizer of the phase of the system? Could one say that the measurement of the conserved charges of particular action would lead to a phase characterized by this action?

See the article Symmetries and Geometry of the “World of Classical Worlds” or the chapter Recent View about K”ahler Geometry and Spin Structure of “World of Classical Worlds”.

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.


Source: http://matpitka.blogspot.com/2023/11/universality-of-holomorphic-solution.html


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