Coulomb correlations do not fill the e'_g hole pockets in Na_{0.3}CoO_2

There exists presently considerable debate over the question whether local Coulomb interactions can explain the absence of the small e'_g Fermi surface hole pockets in photoemission studies of Na_{0.3}CoO_2. By comparing dynamical mean field results for different single particle Hamiltonians and exact diagonalization as well as quantum Monte Carlo treatments, we show that, for realistic values of the Coulomb energy U and Hund exchange J, the e'_g pockets can be slightly enhanced or reduced compared to band structure predictions, but they do not disappear.