24 research outputs found
Holography on local fields via Radon Transform
We define Radon transform and its inverse on the two-dimensional anti-de
Sitter space over local fields using a novel construction through a quadratic
equation over the local field. We show that the holographic bulk reconstruction
of quantum fields in this space can be formulated as the inverse Radon
transform, generalizing the case over the reals, studied earlier.Comment: 1+15 pages LaTeX2e. 1 Figure. A few clarifying comments added.
Version published in JHE
Bulk reconstruction in AdS and Gel'fand-Graev-Radon Transform
The bulk reconstruction formula for a Euclidean anti-de Sitter space is
directly related to the inverse of the Gel'fand-Graev-Radon transform.
Correlation functions of a conformal scalar field theory in the boundary are
thereby related to correlation functions of a self-interacting scalar field
theory in the bulk at different loop orders.Comment: 13 pages, 2 figures, LaTeX. Typos in formulae corrected for measure
factors. Version to Published in JHE
Stabilisation of Seven Directions in an Early Universe M -- theory Model
Our model consists of intersecting 22'55' branes in M theory distributed
uniformly in the common transverse space. Equations of state follow from U
duality symmetries. In this model, three spatial directions expand, and seven
directions stabilise to constant sizes. From string theory perspective, the
dilaton is hence stabilised. The constant sizes depend on certain imbalance
among initial values. One naturally obtains M_{11} \simeq M_s \simeq M_4 and
g_s \simeq 1 within a few orders of magnitude. Smaller numbers, for example M_s
\simeq 10^{- 16} M_4, are also possible but require fine tuning.Comment: 11 Pagesl. Latex file. Version 2: Minor changes and a reference
added. Version 3: Title changed; many textual modifications, mainly to keep
within journal's length constraints, and to explain the differences between
brane gas models and intersecting brane configurations used here; references
added. To appear in Physical Review D (Rapid communications
A note on AdS cosmology and gauge theory correlator
Using AdS/CFT prescription, we compute two point Yang-Mills correlator on a
constant time slice for the Kasner background. Pushing the surface close to the
initial singularity, we find, in some cases, the correlator does not develop
pole. This is consistent with the observations made in a recent work. We
further numerically calculate similar correlator where the bulk is a Kasner AdS
soliton. We find that the qualitative behaviour of the correlator remains
unchanged.Comment: 17 pages, 2 figures, journal versio
10 + 1 to 3 + 1 in an Early Universe with mutually BPS Intersecting Branes
We assume that the early universe is homogeneous, anisotropic, and is
dominated by the mutually BPS 22'55' intersecting branes of M theory. The
spatial directions are all taken to be toroidal. Using analytical and numerical
methods, we study the evolution of such an universe. We find that,
asymptotically, three spatial directions expand to infinity and the remaining
spatial directions reach stabilised values. Any stabilised values can be
obtained by a fine tuning of initial brane densities. We give a physical
description of the stabilisation mechanism. Also, from the perspective of four
dimensional spacetime, the effective four dimensional Newton's constant G_4 is
now time varying. Its time dependence will follow from explicit solutions. We
find in the present case that, asymptotically, G_4 exhibits characteristic log
periodic oscillations.Comment: Latex file, 59 pages, 7 figures. Version 2: A minor correction and a
reference added. Version 3: Critical discussion of the main assumptions is
added in sections I and VIII; two references added. To appear in Physical
Review