211 research outputs found
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
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