Candidates for anti-de Sitter Horizons

We find, from the toric description of the moduli space of D3-branes on non-compact six-dimensional singularities \C^3/\Z_3 and \C^3/\Z_5 in the blown-down limit, the four-dimensional bases on which these singular spaces are complex cones, and prove the existence of K\"ahler-Einstein metrics on these four-dimensional bases. This shows, in particular, that one can use the horizons obtained from these base spaces by a U(1)-foliation as compact parts of the target space for Type-IIB string theory with \ads{5} in the context of the AdS-CFT correspondence.Comment: 16 pages, LATEX2e. Uses times, eepic, amsmath and amssym

Fractional Branes on a Non-compact Orbifold

Fractional branes on the non-compact orbifold \C^3/\Z_5 are studied. First, the boundary state description of the fractional branes are obtained. The open-string Witten index calculated using these states reproduces the adjacency matrix of the quiver of $\Z_5$. Then, using the toric crepant resolution of the orbifold \C^3/\Z_5 and invoking the local mirror principle, B-type branes wrapped on the holomorphic cycles of the resolution are studied. The boundary states corresponding to the five fractional branes are identified as bound states of BPS D-branes wrapping the 0-, 2- and 4-cycles in the exceptional divisor of the resolution of \C^3/\Z_5.Comment: Latex2e, 25 pages, typos corrected, minor modifications, version to appear in JHE