The two-dimensional XY spin glass is studied numerically by a finite size d
efect energy scaling method at T = 0 in the vortex representation which all
ows us to compute the exact (in principle) spin and chiral domain wall ener
gies. We confirm earlier predictions that there is no glass phase at any fi
nite T. Our results strongly support the conjecture that both spin and chir
al order have the same correlation length exponent nu(s) = nu(c) approximat
e to 2.70. Preliminary results in 3D are also obtained.