  Symmetry protected topological (SPT) states are short-range entangled states
with symmetry, which have symmetry protected gapless edge states around a
gapped bulk. Recently, we proposed a systematic construction of SPT phases in
interacting bosonic systems, however it is not very clear what is the form of
the low energy excitations on the gapless edge. In this paper, we answer this
question for two dimensional bosonic SPT phases with Z_N and U(1) symmetry. We
find that while the low energy modes of the gapless edges are non-chiral,
symmetry acts on them in a chiral way, i.e. acts on the right movers and the
left movers differently. This special realization of symmetry protects the
gaplessness of the otherwise unstable edge states by prohibiting a direct
scattering between the left and right movers. Moreover, understanding of the
low energy effective theory leads to experimental predictions about the SPT
phases. In particular, we find that all the 2D U(1) SPT phases have even
integer quantized Hall conductance.
