The basic field equations of TGD allow several dualities. There are 3 of them at the level of basic field equations (and several other dualities such as M^{8}M^{4}× CP_{2} duality).
 The first duality is the analog of particlefield duality. The spacetime surface describing the particle (3surface of M^{4}× CP_{2} instead of pointlike particle) corresponds to the particle aspect and the fields inside it geometrized in terms of submanifold geometry in terms of quantities characterizing geometry of M^{4}× CP_{2} to the field aspect. Particle orbit serves as wave guide for field, one might say.
 Second duality is particlespacetime duality. Particle identified as 3D surface means that particle orbit is spacetime surface glued to a larger spacetime surface by topological sum contacts. It depends on the scale used, whether it is more appropriate to talk about particle or of spacetime.
 The third duality is hydrodynamicsmassless field theory duality Hydrodynamical equations state local conservation of Noether currents. Field equations indeed reduce to local conservation conditions of Noether currents associated with isometries of M^{4}× CP_{2}. One the other hand, these equations have interpretation as nonlinear geometrization of massless wave equation with coupling to Maxwell fields. This realizes the ultimate dream of theoretician: symmetries dictate the dynamics completely. This is expected to be realized also at the level of scattering amplitudes and the generalization of twistor Grassmannian amplitudes could realize this in terms of Yangian symmetry.
Hydrodynamicswave equations duality generalizes to the fermionic sector and involves superconformal symmetry.
 What I call modified gamma matrices are obtained as contractions of the partial derivatives of the action defining spacetime surface with respect to the gradients of imbedding space coordinate with imbedding space gamma matrices. Their divergences vanish by field equations for the spacetime surface and this is necessary for the internal consistency the Dirac equation. The modified gamma matrices reduces to ordinary ones if spacetime surface is M^{4} and one obtains ordinary massless Dirac equation.
 Modified Dirac equation expresses conservation of super current and actually infinite number of super currents obtained by contracting second quantized induced spinor field with the solutions of modified Dirac. This corresponds to the superhydrodynamic aspect. On the other hand, modified Dirac equation corresponds to fermionic analog of massless wave equation as supercounterpart of the nonlinear massless field equation determining spacetime surface.
See the chapter Cosmic string model for the formation of galaxies and stars of "Physics in manysheeted spacetime" or the article article with the same title.
