Recent Developments on the Application of Discrete Symmetries

Abstract

The speaker will talk on his recent works related to discrete symmetries. The Peccei-Quinn symmetry is always approximate whose breaking however is huge due to the QCD anomaly. The dark energy U(1)-global symmetry can be approximated but without the QCD anomaly, which makes it very feeble. It can be small if the discrete symmetry is of high order. He will also give a prospect of the QCD axion detection.