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Lattice chirality: a mission (im)possible?

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As LHC era is coming close, all sorts of ideas about physics beyond the standard model are being explored. It remains possible that a strong-coupling chiral theory could appear at TeV scale. When it comes to strongly coupled theories, lattice is still the most reliable and straightforward regularization method. But defining a chiral gauge theory on the lattice is formidable on its own. In this talk, I will present some most recent theoretical developments in attempt to tackle this problem, and explain some general theorems we proved for generic chiral gauge theories on lattice. These results should be useful in future studies in the field. I will also present some numerical results suggesting that the idea of constructing a chiral gauge theory by decoupling the mirror fermions using a high scale strong- coupling gauge symmetric phase suffers from severe constraints. I will end my talk by a brief outlook on how one may hope to reach a conclusive prove on the feasibility of this idea in general.