  We consider a complex scalar field in (p+3)-dimensional bulk with a negative
cosmological constant and study global vortices in two extra-dimensions. We
reexamine carefully the coupled scalar and Einstein equations, and show that
the boundary value of scalar amplitude at infinity of the extra-dimensions
should be smaller than vacuum expectation value. The brane world has a
cigar-like geometry with an exponentially decaying warp factor and a flat thick
p-brane is embedded. Since a coordinate transformation identifies the obtained
brane world as a black p-brane world bounded by a horizon, this strange
boundary condition of the scalar amplitude is understood as existence of a
short scalar hair.
