C, P and T transformations in QFT, as a pointwise $S^0$ physics theory, are not adequate for modeling the symmetries of baryons and mesons of Standard Model (SM), as a quark / qubit theory based on $S^2$. String Theory (ST), based on $S^1$, is of course the transition theory between the above two types of theories. The symplectic versus complex structure of QFT/CFT reveal the dihedral group $D_4$ as the group of symmetries of the above elementary particles, viewed in the context of the quark model. This point of view introduces Hodge structures as central algebraic structures, which in fact are representations of $U(1)\to SU(2)$, when passing from commutative to non-commutative case. Conformal transformations, i.e. $U(1)$-equivariant, play a central role in quantum theories, like CFT and ST; they are directly related to Hodge structures viewed as representations of $U(1)$.