We derive a geometrical characterisation of a large class of AdS 3 and AdS 2 supersymmetric spacetimes in type IIB supergravity with non-vanishing five-form flux using G-structures. These are obtained as special cases of a class of supersymmetric spacetimes with an R 1,1 or R (time) factor that are associated with D3-branes wrapping calibrated 2-or 3-cycles, respectively, in manifolds with SU(2), SU(3), SU (4) and G 2 holonomy. We show how two explicit AdS solutions, previously constructed in gauged supergravity, satisfy our more general G-structure conditions. For each explicit solution we also derive a special holonomy metric which, although singular, has an appropriate calibrated cycle. After analytic continuation, some of the classes of AdS spacetimes give rise to known classes of BPS bubble solutions with R×SO(4)×SO(4), R×SO(4)×U(1), and R×SO(4) symmetry. These have 1/2, 1/4 and 1/8 supersymmetry, respectively. We present a new class of 1/8 BPS geometries with R × SU(2) symmetry, obtained by analytic continuation of the class of AdS spacetimes associated with D3-branes wrapped on associative three-cycles.
We construct infinite new classes of supersymmetric solutions of D = 11 supergravity that are warped products of AdS 3 with an eight-dimensional manifold M 8 and have non-vanishing four-form flux. In order to be compact, M 8 is constructed as an S 2 bundle over a six-dimensional manifold B 6 which is either Kähler-Einstein or a product of Kähler-Einstein spaces. In the special cases that B 6 contains a twotorus, we also obtain new AdS 3 solutions of type IIB supergravity, with constant dilaton and only five-form flux. Via the AdS-CFT correspondence the solutions with compact M 8 will be dual to two-dimensional conformal field theories with N = (0, 2) supersymmetry. Our construction can also describe non-compact geometries and we discuss examples in type IIB which are dual to four-dimensional N = 1 superconformal theories coupled to string-like defects.
For every positively curved Kähler-Einstein manifold in four dimensions we construct an infinite family of supersymmetric solutions of type IIB supergravity. The solutions are warped products of AdS3 with a compact seven-dimensional manifold and have non-vanishing five-form flux. Via the AdS/CFT correspondence, the solutions are dual to two-dimensional conformal field theories with (0, 2) supersymmetry. The corresponding central charges are rational numbers.Dedicated to Rafael Sorkin in celebration of his 60th birthday.The AdS/CFT correspondence [1] states that any solution of string or M-theory with an AdS d+1 factor should be equivalent to a conformal field theory (CFT) in d spacetime dimensions. This correspondence, and its generalisations, has provided profound insight into the nonperturbative structure of string theory, the structure of quantum field theory and the quantum properties of black holes.Backgrounds with AdS 3 factors are of particular interest because, unlike in higher dimensions, the conformal group in two-dimensions is infinite dimensional. As a consequence two-dimensional conformal field theories are much more tractable than their higher dimensional cousins; for instance, many models are exactly solvable, and there is a considerable literature on the subject. It would be a significant development if, via the AdS/CFT correspondence, string or M-theory can make contact with this large body of work.However, until now there were only a few known explicit AdS 3 × M solutions, with compact M. The most well studied class of examples are the AdS 3 × S 3 × X backgrounds of type IIB supergravity, where X = T 4 or K3. These are dual to N = (4, 4) conformal field theories that are deformations of the sigma model based on the orbifold Sym(X) n /S n . From a string theory perspective, these backgrounds describe the backreaction of a D-brane configuration that can be related to a black hole in five dimensions. It is a remarkable fact that the entropy of this black hole can be precisely derived from the central charge of the dual conformal field theory [2].There have also been recent investigations into the conformal field theory dual to the AdS 3 × S 3 × S 3 × S 1 background of type II string theory [3] (see [4]-[8] for earlier discussions). Despite the fact that the field theory has a larger version of N = (4, 4) superconformal symmetry than those dual to the AdS 3 × S 3 × X solutions, it has proved more difficult to identify them as a number of subtleties arise.The purpose of this letter is to present a new infinite class of supersymmetric AdS 3 backgrounds of type IIB string theory, which are dual to two-dimensional conformal field theories with N = (0, 2) supersymmetry. It will be very interesting if these conformal field theories can be explicitly identified. It will also be very interesting to know whether or not our solutions can be related to black holes.The new solutions are warped products of AdS 3 with a compact seven-dimensional manifold M 7 and have nontrivial self-dual five-form. The manifold...
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