7,089 research outputs found
Spacetime and the Holographic Renormalization Group
Anti-de Sitter (AdS) space can be foliated by a family of nested surfaces
homeomorphic to the boundary of the space. We propose a holographic
correspondence between theories living on each surface in the foliation and
quantum gravity in the enclosed volume. The flow of observables between our
``interior'' theories is described by a renormalization group equation. The
dependence of these flows on the foliation of space encodes bulk geometry.Comment: 12 page
What we don't know about time
String theory has transformed our understanding of geometry, topology and
spacetime. Thus, for this special issue of Foundations of Physics commemorating
"Forty Years of String Theory", it seems appropriate to step back and ask what
we do not understand. As I will discuss, time remains the least understood
concept in physical theory. While we have made significant progress in
understanding space, our understanding of time has not progressed much beyond
the level of a century ago when Einstein introduced the idea of space-time as a
combined entity. Thus, I will raise a series of open questions about time, and
will review some of the progress that has been made as a roadmap for the
future.Comment: 15 pages; Essay for a special issue of Foundations of Physics
commemorating "Forty years of string theory
Deconstruction and Holography
It was recently pointed out that the physics of a single discrete
gravitational extra dimension exhibits a peculiar UV/IR connection relating the
UV scale to the radius of the effective extra dimension. Here we note that this
non-locality is a manifestation of holography, encoding the correct scaling of
the number of fundamental degrees of freedom of the UV theory. This in turn
relates the Wilsonian RG flow in the UV theory to the effective gravitational
dynamics in the extra dimension. The relevant holographic c-function is
determined by the expression for the holographic bound. Holography in this
context is a result of the requirements of unitarity and diffeomorphism
invariance. We comment on the relevance of this observation for the
cosmological constant problem.Comment: 11 pages, LaTe
On the existence of supergravity duals to D1--D5 CFT states
We define a metric operator in the 1/2-BPS sector of the D1-D5 CFT, the
eigenstates of which have a good semi-classical supergravity dual; the
non-eigenstates cannot be mapped to semi-classical gravity duals. We also
analyse how the data defining a CFT state manifests itself in the gravity side,
and show that it is arranged into a set of multipoles. Interestingly, we find
that quantum mechanical interference in the CFT can have observable
manifestations in the semi-classical gravity dual. We also point out that the
multipoles associated to the normal statistical ensemble fluctuate wildly,
indicating that the mixed thermal state should not be associated to a
semi-classical geometry.Comment: 22 pages, 2 figures. v2 : references added, typos correcte
Anti-de Sitter boundary in Poincare coordinates
We study the space-time boundary of a Poincare patch of Anti-de Sitter (AdS)
space. We map the Poincare AdS boundary to the global coordinate chart and show
why this boundary is not equivalent to the global AdS boundary. The Poincare
AdS boundary is shown to contain points of the bulk of the entire AdS space.
The Euclidean AdS space is also discussed. In this case one can define a
semi-global chart that divides the AdS space in the same way as the
corresponding Euclidean Poincare chart.Comment: In this revised version we add a discussion of the physical
consequences of the choice of a coordinate system for AdS space. We changed
figure 1 and added more references. Version to be published in Gen. Relat.
Grav
- …