  It is known as a purely quantum effect that a magnetic flux affects the real
physics of a particle, such as the energy spectrum, even if the flux does not
interfere with the particle's path - the Aharonov-Bohm effect. Here we examine
an Aharonov-Bohm effect on a many-body wavefunction. Specifically, we study
this many-body effect on the gapless edge states of a bulk gapped phase
protected by a global symmetry (such as $\mathbb{Z}_{N}$) - the
symmetry-protected topological (SPT) states. The many-body analogue of spectral
shifts, the twisted wavefunction and the twisted boundary realization are
identified in this SPT state. An explicit lattice construction of SPT edge
states is derived, and a challenge of gauging its non-onsite symmetry is
overcome. Agreement is found in the twisted spectrum between a numerical
lattice calculation and a conformal field theory prediction.
