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We measure the evolution of the specific star formation rate (sSFR = SFR /Mstellar) between redshift 4 and 6 to investigate the previous reports of"constant" sSFR at z>2. We obtain photometry on a large sample of galaxies atz~4-6 located in the GOODS-S field that have high quality imaging from HST andSpitzer. We have derived stellar masses and star formation rates (SFRs) throughstellar population modeling of their spectral energy distributions (SEDs). Weestimate the dust extinction from the observed UV colors. In the SED fittingprocess we have studied the effects of assuming a star formation history (SFH)both with constant SFR and one where the SFR rises exponentially with time. Thelatter SFH is chosen to match the observed evolution of the UV luminosityfunction. We find that neither the mean SFRs nor the mean stellar masses changesignificantly when the rising SFR (RSF) model is assumed instead of theconstant SFR model. When focusing on galaxies with Mstar ~ 5x10^9 Msun, we findthat the sSFR evolves weakly with redshift (sSFR(z) \propto (1+z)^(0.6+/-0.1)Gyr^-1), consistent with previous results and with recent estimates of the sSFRat z~2-3 using similar assumptions. We have also investigated the impact ofoptical emission lines on our results. We estimate that the contribution ofemission lines to the rest-frame optical fluxes is only modest at z~4 and 5 butit could reach ~50% at z~6. When emission lines of this strength are taken intoaccount, the sSFR shows somewhat higher values at high redshifts, according tothe relation sSFR(z) \propto (1+z)^(1.0+/-0.1) Gyr^-1, i.e., ~2.3x higher atz~6 than at z~2. However, the observed evolution is substantially weaker thanthat found at z<2 or that expected from current models (which corresponds tosSFR(z) \propto (1+z)^(2.5) Gyr^-1). -abridged-

Slow Evolution of the Specific Star Formation Rate at z>2: The Impact of Dust, Emission Lines, and A Rising Star Formation History