Gapless boundary excitations in the quantum Hall states and in the chiral spin states

Using the gauge invariances, I show that the (fractional and integral) quantum Hall states and the chiral spin states must have gapless boundary excitations. The dynamical properties of those gapless excitations are studied. Under some general assumptions, the gapless excitations are shown to form a representation of the U(1) or SU(2) Kac-Moody algebras and to contribute to a specific heat with a linear temperature dependence. The low-energy effective theories for those gapless excitations are derived. The quantum numbers of the gapless boundary excitations are also discussed. In particular, the charge-zero sector of the low-lying boundary excitations in the fractional quantum Hall states are shown to be described by the charge-zero sector of free fermions with fractional charges.