We present a quantitative spectral analysis of five very massive stars in the
Arches cluster, located near the Galactic center, to determine stellar
parameters, stellar wind properties and, most importantly, metallicity content.
The analysis uses a new technique, presented here for the first time, and uses
line-blanketed NLTE wind/atmosphere models fit to high-resolution near-infrared
spectra of late-type nitrogen-rich Wolf-Rayet stars and OfI+ stars in the
cluster. It relies on the fact that massive stars reach a maximum nitrogen
abundance that is related to initial metallicity when they are in the WNL
phase. We determine the present-day nitrogen abundance of the WNL stars in the
Arches cluster to be 1.6% (mass fraction) and constrain the stellar metallicity
in the cluster to be solar. This result is invariant to assumptions about the
mass-luminosity relationship, the mass-loss rates, and rotation speeds. In
addition, from this analysis, we find the age of the Arches cluster to be
2-2.5Myr, assuming coeval formation