Adiabaticity and emergence of classical space-time in time-dependent matrix theories

We discuss the low-curvature regime of time-dependent matrix theories proposed to describe non-perturbative quantum gravity in asymptotically plane-wave space-times. The emergence of near-classical space-time in this limit turns out to be closely linked to the adiabaticity of the matrix theory evolution. Supersymmetry restoration at low curvatures, which is crucial for the usual space-time interpretation of matrix theories, becomes an obvious feature of the adiabatic regime.Comment: 18 pages; v2: disclaimers and references added, version for publicatio

A Hidden Symmetry of AdS Resonances

Recent investigations have revealed powerful selection rules for resonant energy transfer between modes of non-linear perturbations in global anti-de Sitter (AdS) space-time. It is likely that these selection rules are due to the highly symmetric nature of the underlying AdS background, though the precise relation has remained unclear. In this article, we demonstrate that the equation satisfied by the scalar field mode functions in AdS(d+1) has a hidden SU(d) symmetry, and explicitly specify the multiplets of this SU(d) symmetry furnished by the mode functions. We also comment on the role this structure might play in explaining the selection rules.Comment: 12 pages; v2: minor improvements, published versio

Detailed ultraviolet asymptotics for AdS scalar field perturbations

We present a range of methods suitable for accurate evaluation of the leading asymptotics for integrals of products of Jacobi polynomials in limits when the degrees of some or all polynomials inside the integral become large. The structures in question have recently emerged in the context of effective descriptions of small amplitude perturbations in anti-de Sitter (AdS) spacetime. The limit of high degree polynomials corresponds in this situation to effective interactions involving extreme short-wavelength modes, whose dynamics is crucial for the turbulent instabilities that determine the ultimate fate of small AdS perturbations. We explicitly apply the relevant asymptotic techniques to the case of a self-interacting probe scalar field in AdS and extract a detailed form of the leading large degree behavior, including closed form analytic expressions for the numerical coefficients appearing in the asymptotics.Comment: v2: 19 pages, expanded version accepted to JHE