After procrastinating for almost a year, I finally finished this paper. It is going to be recognized as a new milestone on mirror matter studies. In particular, amazing connections between string theory and new supersymmetric mirror models are established. Mirror symmetry as a fundamental concept is deeply examined. Based on mathematical results from string theory, we can finally put these mirror models on a firmer and self-consistent ground and can really explain an impressive list of puzzles in fundamental physics and cosmology. Without further ado, here it is:
The two discrete generators of the full Lorentz group O(1,3) in 4D spacetime are typically chosen to be parity inversion symmetry P and time reversal symmetry T, which are responsible for the four topologically separate components of O(1,3). Under general considerations of quantum field theory (QFT) with internal degrees of freedom, mirror symmetry is a natural extension of P, while CP symmetry resembles T in spacetime. In particular, mirror symmetry is critical as it doubles the full Dirac fermion representation in QFT and essentially introduces a new sector of mirror particles. Its close connection to T-duality and Calabi-Yau mirror symmetry in string theory is clarified. Extension beyond the Standard model can then be constructed using both left- and right-handed heterotic strings guided by mirror symmetry. Many important implications such as supersymmetry, chiral anomalies, topological transitions, Higgs, neutrinos, and dark energy, are discussed.