619 research outputs found
Equilibration in low-dimensional quantum matrix models
Matrix models play an important role in studies of quantum gravity, being
candidates for a formulation of M-theory, but are notoriously difficult to
solve. In this work, we present a fresh approach by introducing a novel exact
model provably equivalent with low-dimensional bosonic matrix models. In this
equivalent model significant local structure becomes apparent and it can serve
as a simple toy model for analytical and precise numerical study. We derive a
substantial part of the low energy spectrum, find a conserved charge, and are
able to derive numerically the Regge trajectories. To exemplify the usefulness
of the approach, we address questions of equilibration starting from a
non-equilibrium situation, building upon an intuition from quantum information.
We finally discuss possible generalizations of the approach.Comment: 5+2 pages, 2 figures; v2: published versio
Generalized Conformal Symmetry and Oblique AdS/CFT Correspondence for Matrix Theory
The large N behavior of Matrix theory is discussed on the basis of the
previously proposed generalized conformal symmetry. The concept of `oblique'
AdS/CFT correspondence, in which the conformal symmetry involves both the
space-time coordinates and the string coupling constant, is proposed. Based on
the explicit predictions for two-point correlators, possible implications for
the Matrix-theory conjecture are discussed.Comment: LaTeX, 10 pages, 2 figures, written version of the talk presented at
Strings'9
Semidefinite Representation of the -Ellipse
The -ellipse is the plane algebraic curve consisting of all points whose
sum of distances from given points is a fixed number. The polynomial
equation defining the -ellipse has degree if is odd and degree
if is even. We express this polynomial equation as
the determinant of a symmetric matrix of linear polynomials. Our representation
extends to weighted -ellipses and -ellipsoids in arbitrary dimensions,
and it leads to new geometric applications of semidefinite programming.Comment: 16 pages, 5 figure
Census Taking in the Hat: FRW/CFT Duality
In this paper a holographic description of eternal inflation is developed. We
focus on the description of an open FRW universe that results from a tunneling
event in which a false vacuum with positive vacuum energy decays to a
supersymmetric vacuum with vanishing cosmological constant. The observations of
a "Census Taker" in the final vacuum can be organized into a holographic dual
conformal field theory that lives on the asymptotic boundary of space. We refer
to this bulk-boundary correspondence as FRW/CFT duality. The dual CFT is a
Euclidean two-dimensional theory that includes a Liouville 2-D gravity sector
describing geometric fluctuations of the boundary. The RG flow of the theory is
richer than in the ADS/CFT correspondence, and generates two space-time
dimensions--one space-like and one time-like. We discuss a number of phenomena
such as bubble collisions, and the Garriga, Guth, Vilenkin "persistence of
memory," from the dual viewpoint.Comment: 71 pages, 16 figures. A preliminary version of the ideas in this
paper was reported in arXiv:0710.1129; v2: Corrected a typo in eq. (5.21)
Future Foam
We study pocket universes which have zero cosmological constant and
non-trivial boundary topology. These arise from bubble collisions in eternal
inflation. Using a simplified dust model of collisions we find that boundaries
of any genus can occur. Using a radiation shell model we perform analytic
studies in the thin wall limit to show the existence of geometries with a
single toroidal boundary. We give plausibility arguments that higher genus
boundaries can also occur. In geometries with one boundary of any genus a
timelike observer can see the entire boundary. Geometries with multiple
disconnected boundaries can also occur. In the spherical case with two
boundaries the boundaries are separated by a horizon. Our results suggest that
the holographic dual description for eternal inflation, proposed by Freivogel,
Sekino, Susskind and Yeh, should include summation over the genus of the base
space of the dual conformal field theory. We point out peculiarities of this
genus expansion compared to the string perturbation series.Comment: 23 pages, 6 figure
Nonlocality vs. complementarity: a conservative approach to the information problem
A proposal for resolution of the information paradox is that "nice slice"
states, which have been viewed as providing a sharp argument for information
loss, do not in fact do so as they do not give a fully accurate description of
the quantum state of a black hole. This however leaves an information
*problem*, which is to provide a consistent description of how information
escapes when a black hole evaporates. While a rather extreme form of
nonlocality has been advocated in the form of complementarity, this paper
argues that is not necessary, and more modest nonlocality could solve the
information problem. One possible distinguishing characteristic of scenarios is
the information retention time. The question of whether such nonlocality
implies acausality, and particularly inconsistency, is briefly addressed. The
need for such nonlocality, and its apparent tension with our empirical
observations of local quantum field theory, may be a critical missing piece in
understanding the principles of quantum gravity.Comment: 11 pages of text and figures, + references. v2 minor text. v3 small
revisions to match final journal versio
Scalar Three-point Functions in a CDL Background
Motivated by the FRW-CFT proposal by Freivogel, Sekino, Susskind and Yeh, we
compute the three-point function of a scalar field in a Coleman-De Luccia
instanton background. We first compute the three-point function of the scalar
field making only very mild assumptions about the scalar potential and the
instanton background. We obtain the three-point function for points in the FRW
patch of the CDL instanton and take two interesting limits; the limit where the
three points are near the boundary of the hyperbolic slices of the FRW patch,
and the limit where the three points lie on the past lightcone of the FRW
patch. We expand the past lightcone three-point function in spherical
harmonics. We show that the near boundary limit expansion of the three-point
function of a massless scalar field exhibits conformal structure compatible
with FRW-CFT when the FRW patch is flat. We also compute the three-point
function when the scalar is massive, and explain the obstacles to generalizing
the conjectured field-operator correspondence of massless fields to massive
fields.Comment: 42 pages + appendices, 10 figures; v2, v3: minor correction
Anisotropic scale invariant cosmology
We study a possibility of anisotropic scale invariant cosmology. It is shown
that within the conventional Einstein gravity, the violation of the null energy
condition is necessary. We construct an example based on a ghost condensation
model that violates the null energy condition. The cosmological solution
necessarily contains at least one contracting spatial direction as in the
Kasner solution. Our cosmology is conjectured to be dual to, if any, a
non-unitary anisotropic scale invariant Euclidean field theory. We investigate
simple correlation functions of the dual theory by using the holographic
computation. After compactification of the contracting direction, our setup may
yield a dual field theory description of the winding tachyon condensation that
might solve the singularity of big bang/crunch of the universe.Comment: 12 pages, v2: reference adde
Penrose Limit and String Theories on Various Brane Backgrounds
We investigate the Penrose limit of various brane solutions including
Dp-branes, NS5-branes, fundamental strings, (p,q) fivebranes and (p,q) strings.
We obtain special null geodesics with the fixed radial coordinate (critical
radius), along which the Penrose limit gives string theories with constant
mass. We also study string theories with time-dependent mass, which arise from
the Penrose limit of the brane backgrounds. We examine equations of motion of
the strings in the asymptotic flat region and around the critical radius. In
particular, for (p,q) fivebranes, we find that the string equations of motion
in the directions with the B field are explicitly solved by the spheroidal wave
functions.Comment: 41 pages, Latex, minor correction
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