Planetary nebulae in the inner Milky Way

New abundances of planetary nebulae located towards the bulge of the Galaxy are derived based on observations made at LNA (Brazil). We present accurate abundances of the elements He, N, S, O, Ar, and Ne for 56 PNe located towards the galactic bulge. The data shows a good agreement with other results in the literature, in the sense that the distribution of the abundances is similar to those works. From the statistical analysis performed, we can suggest a bulge-disk interface at 2.2 kpc for the intermediate mass population, marking therefore the outer border of the bulge and inner border of the disk.Comment: 2 pages, 1 figure, uses iaus.cls, in press, IAU Symp. 265, Chemical abundances in the Universe: Connecting the first Stars to Planets, Ed. K. Cunha, M. Spite, B. Barbu

Minimal string-scale unification of gauge couplings

We look for the minimal particle content which is necessary to add to the standard model in order to have a complete unification of gauge couplings and gravity at the weakly coupled heterotic string scale. Using the current precision electroweak data, we find that the presence of a vector-like fermion at an intermediate scale and a non-standard hypercharge normalization are in general sufficient to achieve this goal at two-loop level. If one requires the extra matter scale to be below the TeV scale, then it is found that the addition of three vector-like fermion doublets with a mass around 700 GeV yields a perfect string-scale unification, provided that the affine levels are kY=13/3, k2=1 and k3=2, as in the SU(5) X SU(5) string-GUT. Furthermore, if supersymmetry is broken at the unification scale, the Higgs mass is predicted in the range 125 GeV - 170 GeV, depending on the precise values of the top quark mass and tan(beta) parameter.Comment: 12 pages, 2 figures, references updated and comments added, final version to appear in Phys. Lett.