We present deep Keck/LRIS spectroscopy and HST/WFC3 imaging in the rest-frame optical for a sample of eight galaxies at z \sim 1.5 with high photometrically-determined stellar masses .
The data are combined with VLT/XShooter spectra of five galaxies from van de Sande et al .
( 2011 , 2012 to be submitted ) .
We find that these thirteen galaxies have high velocity dispersions , with a median of \sigma = 301 \mathrm { km s ^ { -1 } } .
This high value is consistent with their relatively high stellar masses and compact sizes .
We study their stellar populations using the strength of Balmer absorption lines , which are not sensitive to dust absorption .
We find a large range in Balmer absorption strength , with many galaxies showing very strong lines indicating young ages .
The median \mathrm { H \delta _ { A } } equivalent width , determined directly or inferred from the H10 line , is 5.4 Å , indicating a luminosity-weighted age of \sim 1 Gyr .
Although this value may be biased towards higher values because of selection effects , high-dispersion galaxies with such young ages are extremely rare in the local Universe .
Interestingly we do not find a simple correlation with rest-frame U - V color : some of the reddest galaxies have very strong Balmer absorption lines .
These results demonstrate that many high-dispersion galaxies at z \sim 1.5 were quenched recently .
This implies that there must be a population of star-forming progenitors at z \sim 2 with high velocity dispersions or linewidths , which are notoriously absent from CO/H \alpha selected surveys .