Timelike reduction and T-duality

Abstract

In the light of recent developments in Superstring Theory, it has become of interest to study Kaluza-Klein dimensional reduction of supergravities not only on spatial manifolds, but also on the time direction. We study a particularly relevant class of solutions that admit timelier reductions, involving the product of anti-do Sitter (AdS) spacetimes with spheres. These AdS spacetimes can be described as liber bundles over non compact versions of CP[], the complex projective spaces, where time is the coordinate on the fibers. This allows lifelike reductions to be performed, in a manner analogous to that in AdS₅ x S⁵, except that now it is the AdS that is Hopf reduced, rather than the sphere. In order to study the supersymmetry, we derive general expressions for the Killing sailors in Anti-de Sitter spacetime of odd dimension with respect to the field reparametrization in the bosonic sector. In addition, we perform Kaluza-Klein reduction along the time direction of D = 10 type IIB theory to D = 9. Then, the T-duality relation links D = 9 type IIB to a new D = 9 type IIA. theory. We oxidize D = 9 type IIA* to the D = 10 type IIA* theory, and finally write its explicit solution.