3 research outputs found
New non compact Calabi-Yau metrics in D=6
A method for constructing explicit Calabi-Yau metrics in six dimensions in
terms of an initial hyperkahler structure is presented. The equations to solve
are non linear in general, but become linear when the objects describing the
metric depend on only one complex coordinate of the hyperkahler 4-dimensional
space and its complex conjugated. This situation in particular gives a dual
description of D6-branes wrapping a complex 1-cycle inside the hyperkahler
space, which was studied by Fayyazuddin. The present work generalize the
construction given by him. But the explicit solutions we present correspond to
the non linear problem. This is a non linear equation with respect to two
variables which, with the help of some specific anzatz, is reduced to a non
linear equation with a single variable solvable in terms of elliptic functions.
In these terms we construct an infinite family of non compact Calabi-Yau
metrics.Comment: A numerical error has been corrected together with the corresponding
analysis of the metri
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