ABSTRACTS
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Quantum TGD should be reducible to the classical spinor geometry of the configuration space ("world of classical worlds" (WCW)). The possibility to express the components of WCW Kähler metric as anticommutators of WCW gamma matrices becomes a practical tool if one assumes that WCW gamma matrices correspond to Noether super charges for supersymplectic algebra of WCW. The possibility to express the Kähler metric also in terms of Kähler function identified as Kähler for Euclidian spacetime regions leads to a duality analogous to AdS/CFT duality. Physical states should correspond to the modes of the WCW spinor fields and the identification of the fermionic oscillator operators as supersymplectic charges is highly attractive. WCW spinor fields cannot, as one might naively expect, be carriers of a definite spin and unit fermion number. Concerning the construction of the WCW spinor structure there are some important clues. 1. Geometrization of fermionic statistics in terms of configuration space spinor structure The great vision has been that the second quantization of the induced spinor fields can be understood geometrically in terms of the WCW spinor structure in the sense that the anticommutation relations for WCW gamma matrices require anticommutation relations for the oscillator operators for free second quantized induced spinor fields.
2. KählerDirac equation for induced spinor fields Supersymmetry between fermionic and and WCW degrees of freedom dictates that KählerDirac action is the unique choice for the Dirac action There are several approaches for solving the modified Dirac (or KählerDirac) equation.

Khovanov homology generalizes the Jones polynomial as knot invariant. The challenge is to find a quantum physical construction of Khovanov homology analous to the topological QFT defined by ChernSimons action allowing to interpret Jones polynomial as vacuum expectation value of Wilson loop in nonAbelian gauge theory. Witten's approach to Khovanov homology relies on fivebranes as is natural if one tries to define 2knot invariants in terms of their cobordisms involving violent unknottings. Despite the difference in approaches it is very useful to try to find the counterparts of this approach in quantum TGD since this would allow to gain new insights to quantum TGD itself as almost topological QFT identified as symplectic theory for 2knots, braids and braid cobordisms. This comparison turns out to be extremely useful from TGD point of view. An essentially unique identification of string world sheets and therefore also of the braids whose ends carry quantum numbers of many particle states at partonic 2surfaces emerges if one identifies the string word sheets as singular surfaces in the same manner as is done in Witten's approach. Even more, the conjectured slicings of preferred extremals by 3D surfaces and string world sheets central for quantum TGD can be identified uniquely. The slicing by 3surfaces would be interpreted in gauge theory in terms of Higgs= constant surfaces with radial coordinate of CP_{2} playing the role of Higgs. The slicing by string world sheets would be induced by different choices of U(2) subgroup of SU(3) leaving Higgs=constant surfaces invariant. Also a physical interpretation of the operators Q, F, and P of Khovanov homology emerges. P would correspond to instanton number and F to the fermion number assignable to right handed neutrinos. The breaking of M^{4} chiral invariance makes possible to realize Q physically. The finding that the generalizations of Wilson loops can be identified in terms of the gerbe fluxes ∫ H_{A} J supports the conjecture that TGD as almost topological QFT corresponds essentially to a symplectic theory for braids and 2knots.
