Symplectic potentials and resolved Ricci-flat ACG metrics

We pursue the symplectic description of toric Kahler manifolds. There exists a general local classification of metrics on toric Kahler manifolds equipped with Hamiltonian two-forms due to Apostolov, Calderbank and Gauduchon(ACG). We derive the symplectic potential for these metrics. Using a method due to Abreu, we relate the symplectic potential to the canonical potential written by Guillemin. This enables us to recover the moment polytope associated with metrics and we thus obtain global information about the metric. We illustrate these general considerations by focusing on six-dimensional Ricci flat metrics and obtain Ricci flat metrics associated with real cones over L^{pqr} and Y^{pq} manifolds. The metrics associated with cones over Y^{pq} manifolds turn out to be partially resolved with two blowup parameters taking special (non-zero)values. For a fixed Y^{pq} manifold, we find explicit metrics for several inequivalent blow-ups parametrised by a natural number k in the range 0<k<p. We also show that all known examples of resolved metrics such as the resolved conifold and the resolution of C^3/Z_3 also fit the ACG classification.Comment: LaTeX, 34 pages, 4 figures (v2)presentation improved, typos corrected and references added (v3)matches published versio

Supersymmetric AdS_5 Solutions of Type IIB Supergravity

We analyse the most general bosonic supersymmetric solutions of type IIB supergravity whose metrics are warped products of five-dimensional anti-de Sitter space AdS_5 with a five-dimensional Riemannian manifold M_5. All fluxes are allowed to be non-vanishing consistent with SO(4,2) symmetry. We show that the necessary and sufficient conditions can be phrased in terms of a local identity structure on M_5. For a special class, with constant dilaton and vanishing axion, we reduce the problem to solving a second order non-linear ODE. We find an exact solution of the ODE which reproduces a solution first found by Pilch and Warner. A numerical analysis of the ODE reveals an additional class of local solutions.Comment: 33 page