Hubble Space Telescope and Spitzer Observations of the Afterglow and Host Galaxy of GRB 050904 at z = 6.295

We present deep Hubble Space Telescope (HST ) and Spitzer Space Telescope observations of GRB 050904 at z = 6:295. We detect the afterglow in the H band more than 3 weeks after the burst and confirm the presence of a jet break at t ≈ 2:1 days. This leads to an estimated opening angle of about 4° and a beaming-corrected energy of about 10^(51) ergs, similar to those of lower redshift gamma-ray bursts (GRBs). We do not detect an underlying host galaxy with either HST or Spitzer. From the upper limits we infer an extinction-corrected absolute magnitude M_(UV) ≳ -20:3 mag, or L ≾ L^*, a star formation rate of ≾ 5.7M_⊙ yr^(-1), and a stellar mass of ≾ few x 10^9 M_⊙. A comparison to spectroscopically confirmed galaxies at z > 5:5 reveals that the host of GRB 050904 is fainter and has a lower star formation rate than at least 80% of these objects. Finally, using our luminosity limits, and the metallicity of about 0.05 Z_⊙ inferred from the afterglow absorption spectrum, we place the first limit on the luminosity-metallicity relation at z > 6. Future afterglow and host galaxy observations of z ≳ 4 GRBs should elucidate whether the mass- and luminosity-metallicity relations continue to evolve beyond the present limits of z ≾ 2.