Plane Waves and Vacuum Interpolation

A 1 2 -BPS family of time dependent plane wave spacetimes which give rise to exactly solvable string backgrounds is presented. In particular a solution which interpolates between Minkowski spacetime and the maximally supersymmetric homogeneous plane wave along a timelike direction is analyzed. We work in d = 4, N = 2 supergravity, but the results can be easily extended to d = 10, 11. The conformal boundary of a particular class of solutions is studied. [email protected] Introduction Since the discovery of the maximally supersymmetric plane wave solution in type IIB theory [1], great progress has been achieved in the AdS/CFT context in going beyond the supergravity approximation [2]. It is known that pp-waves yield exact classical backgrounds for string theory since all curvature invariants vanish and therefore receive no α′ corrections. Hence, pp-wave spacetimes correspond to exact conformal field theories. This fact has been known for some time [3], and after the work of [4] the interest in them has been revived. Plane waves in particular provide simple toy models for studying string propagation and singularity issues because it has been shown that they lead to exactly solvable models in the light cone gauge [5] (see also [6]). After reviewing how to obtain the maximally supersymmetric solutions of d = 4, N = 2 supergravity in sections 1 and 2, we present the 12 -BPS time dependent pp-wave backgrounds in section 3. In section 4 we develop a general method to study the conformal boundary of these time dependent solutions and then for a particular class of metrics the boundary is analyzed. We end with some conclusions and directions for future research. 1 Constraints from Maximal Supersymmetry We first review the spacetimes of d = 4, N = 2 supergravity with maximal supersymmetry, this means spacetimes with 8 Killing spinors. The Killing spinor equation is [7] ∇̂ξ ≡ (d+ 1 4 ω − i 4 6FΓ)ξ = 0, (1) where d = ∂μ dx , ω = ω ab μ Γab dx , 6F = F Γab and Γ = Γa eμdx. Maximal supersymmetry implies that the commutator of covariant derivatives as a spinor matrix must vanish [