We have carried out a deep narrow-band imaging survey of six fields with heavy-element quasar absorption lines, using the Goddard Fabry-Perot (FP) system at the Apache Point Observatory (APO) 3.5-meter telescope. The aim of these observations was to search for redshifted Ly-$alpha$ emission from the galaxies underlying the absorbers at $z = 2.3-2.5$ and their companion galaxies. The 3 $sigma$ sensitivity levels ranged between $1.9 times 10^{-17}$ and $5.4 times 10^{-17}$ erg s$^{-1}$ cm$^{-2}$ in observed-frame Ly-$alpha$ flux. No significant Ly-$alpha$ emitters were detected at $> 3 sigma$ level. The absence of significant Ly-$alpha$ emission implies limits on the star formation rate (SFR) of 0.9-2.7 $M_{odot}$ yr$^{-1}$ per 2-pixel x 2-pixel region, if no dust attenuation is assumed. We compare our results with those from other emission-line studies of absorber fields and with predictions for global average SFR based on the models of cosmic chemical evolution. Our limits are among the tightest existing constraints on Ly-$alpha$ emission from galaxies in absorber fields, but are consistent with many other studies. In the absence of dust attenuation, these studies suggest that SFRs in a large fraction of objects in the absorber fields may lie below the global mean SFR. However, it is possible that dust attenuation is responsible for the low emission line fluxes in some objects. It is also possible that the star-forming regions are compact and at smaller angular separations from the quasar than the width of our point spread function and, get lost in the quasar emission. We outline future observations that could help to distinguish between the various possibilities.
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