  We propose a model with the left-handed and right-handed continuous Abelian
gauge symmetry; $U(1)_L\times U(1)_R$. Then three right-handed neutrinos are
naturally required to achieve $U(1)_R$ anomaly cancellations, while several
mirror fermions are also needed to do $U(1)_L$ anomaly cancellations. Then we
formulate the model, and discuss its testability of the new gauge interactions
at collider physics such as the large hadron collider (LHC) and the
international linear collider (ILC). In particular, we can investigate chiral
structure of the interactions by the analysis of forward-backward asymmetry
based on polarized beam at the ILC.
