15,030 research outputs found
The triviality bound on the Higgs mass; its value and what it means
Older lattice work exploring the Higgs mass triviality bound is briefly
reviewed. It indicates that a strongly interacting scalar sector in the minimal
standard model cannot exist; on the other hand low energy QCD phenomenology
might be interpreted as an indication that it could. We attack this puzzle
using the expansion and discover a simple criterion for selecting a
lattice action that is more likely to produce a heavy Higgs particle. Depending
on the precise form of the limitation put on the cutoff effects, our large
calculations, when combined with old numerical data, suggest that the Higgs
mass bound might be around 750 , which is higher than the
previously obtained. Preliminary numerical work indicates that an increase of
at least 19\% takes place at on the lattice when the old simple
action is replaced with a new action (still containing only nearest neighbor
interactions) if one uses the lattice spacing as the physical cutoff for both
actions. It appears that, while a QCD like theory could produce , a meaningful ``minimal elementary Higgs'' theory cannot have M_H/ F~
\gtapprox 3. Still, even at 750 , the Higgs particle is so wide (GeV), that one cannot argue any more that the scalar sector is weakly
coupled.Comment: 8 pages. Latex file with 4 ps figures included. Preprint RU-92-22,
SCRI-92-11
Conceptual Unification of Gravity and Quanta
We present a model unifying general relativity and quantum mechanics. The
model is based on the (noncommutative) algebra \mbox{{\cal A}} on the groupoid
\Gamma = E \times G where E is the total space of the frame bundle over
spacetime, and G the Lorentz group. The differential geometry, based on
derivations of \mbox{{\cal A}}, is constructed. The eigenvalue equation for the
Einstein operator plays the role of the generalized Einstein's equation. The
algebra \mbox{{\cal A}}, when suitably represented in a bundle of Hilbert
spaces, is a von Neumann algebra \mathcal{M} of random operators representing
the quantum sector of the model. The Tomita-Takesaki theorem allows us to
define the dynamics of random operators which depends on the state \phi . The
same state defines the noncommutative probability measure (in the sense of
Voiculescu's free probability theory). Moreover, the state \phi satisfies the
Kubo-Martin-Schwinger (KMS) condition, and can be interpreted as describing a
generalized equilibrium state. By suitably averaging elements of the algebra
\mbox{{\cal A}}, one recovers the standard geometry of spacetime. We show that
any act of measurement, performed at a given spacetime point, makes the model
to collapse to the standard quantum mechanics (on the group G). As an example
we compute the noncommutative version of the closed Friedman world model.
Generalized eigenvalues of the Einstein operator produce the correct components
of the energy-momentum tensor. Dynamics of random operators does not ``feel''
singularities.Comment: 28 LaTex pages. Substantially enlarged version. Improved definition
of generalized Einstein's field equation
Lattice quark propagator with staggered quarks in Landau and Laplacian gauges
We report on the lattice quark propagator using standard and improved
Staggered quark actions, with the standard, Wilson gauge action. The standard
Kogut-Susskind action has errors of \oa{2} while the ``Asqtad'' action has
\oa{4}, \oag{2}{2} errors. The quark propagator is interesting for studying the
phenomenon of dynamical chiral symmetry breaking and as a test-bed for
improvement. Gauge dependent quantities from lattice simulations may be
affected by Gribov copies. We explore this by studying the quark propagator in
both Landau and Laplacian gauges. Landau and Laplacian gauges are found to
produce very similar results for the quark propagator.Comment: 11 pages, 15 figure
Dissipative Bjorken hydrodynamics from an AdS Schwarzschild black hole
We discuss the derivation of dissipative Bjorken hydrodynamics from a
Schwarzschild black hole in asymptotically AdS spacetime of arbitrary dimension
in the limit of large longitudinal proper time . Using an appropriate
slicing near the boundary, we calculate the Schwarzschild metric to
next-to-next-to-leading order in the large expansion as well as the dual
stress-energy tensor on the boundary via holographic renormalization. At
next-to-next-to-leading order, it is necessary to perturb the Schwarzschild
metric in order to maintain boost invariance. The perturbation has a power law
time dependence and leads to the same value of the ratio of viscosity to
entropy density, , as in the case of sinusoidal perturbations. Our
results are in agreement with known time-dependent asymptotic solutions of the
Einstein equations in five dimensions.Comment: 13 pages, improved discussion of singularities, version to appear in
Phys. Rev.
The characteristics of thermalization of boost-invariant plasma from holography
We report on the approach towards the hydrodynamic regime of boost-invariant
N=4 super Yang-Mills plasma at strong coupling starting from various
far-from-equilibrium states at tau=0. The results are obtained through
numerical solution of Einstein's equations for the dual geometries, as
described in detail in the companion article arXiv:1203.0755. Despite the very
rich far-from-equilibrium evolution, we find surprising regularities in the
form of clear correlations between initial entropy and total produced entropy,
as well as between initial entropy and the temperature at thermalization,
understood as the transition to a hydrodynamic description. For 29 different
initial conditions that we consider, hydrodynamics turns out to be definitely
applicable for proper times larger than 0.7 in units of inverse temperature at
thermalization. We observe a sizable anisotropy in the energy-momentum tensor
at thermalization, which is nevertheless entirely due to hydrodynamic effects.
This suggests that effective thermalization in heavy ion collisions may occur
significantly earlier than true thermalization.Comment: 4 pages, 5 figures; see also the companion article arXiv:1203.0755;
v2: figure corrected (fixes problem with Acrobat); v3: various clarifications
and additional data points added; v4: typo fixed, publishe
Black brane entropy and hydrodynamics: the boost-invariant case
The framework of slowly evolving horizons is generalized to the case of black
branes in asymptotically anti-de Sitter spaces in arbitrary dimensions. The
results are used to analyze the behavior of both event and apparent horizons in
the gravity dual to boost-invariant flow. These considerations are motivated by
the fact that at second order in the gradient expansion the hydrodynamic
entropy current in the dual Yang-Mills theory appears to contain an ambiguity.
This ambiguity, in the case of boost-invariant flow, is linked with a similar
freedom on the gravity side. This leads to a phenomenological definition of the
entropy of black branes. Some insights on fluid/gravity duality and the
definition of entropy in a time-dependent setting are elucidated.Comment: RevTeX, 42 pages, 4 figure
Modelling the quark propagator
The quark propagator is at the core of lattice hadron spectrum calculations
as well as studies in other nonperturbative schemes. We investigate the quark
propagator with an improved staggered action (Asqtad) and an improved gluon
action, which provides good quality data down to small quark masses. This is
used to construct ans\"{a}tze suitable for model hadron calculations as well as
adding to our intuitive understanding of QCD.Comment: Lattice2002(spectrum
Entanglement, Holography and Causal Diamonds
We argue that the degrees of freedom in a d-dimensional CFT can be
re-organized in an insightful way by studying observables on the moduli space
of causal diamonds (or equivalently, the space of pairs of timelike separated
points). This 2d-dimensional space naturally captures some of the fundamental
nonlocality and causal structure inherent in the entanglement of CFT states.
For any primary CFT operator, we construct an observable on this space, which
is defined by smearing the associated one-point function over causal diamonds.
Known examples of such quantities are the entanglement entropy of vacuum
excitations and its higher spin generalizations. We show that in holographic
CFTs, these observables are given by suitably defined integrals of dual bulk
fields over the corresponding Ryu-Takayanagi minimal surfaces. Furthermore, we
explain connections to the operator product expansion and the first law of
entanglement entropy from this unifying point of view. We demonstrate that for
small perturbations of the vacuum, our observables obey linear two-derivative
equations of motion on the space of causal diamonds. In two dimensions, the
latter is given by a product of two copies of a two-dimensional de Sitter
space. For a class of universal states, we show that the entanglement entropy
and its spin-three generalization obey nonlinear equations of motion with local
interactions on this moduli space, which can be identified with Liouville and
Toda equations, respectively. This suggests the possibility of extending the
definition of our new observables beyond the linear level more generally and in
such a way that they give rise to new dynamically interacting theories on the
moduli space of causal diamonds. Various challenges one has to face in order to
implement this idea are discussed.Comment: 84 pages, 12 figures; v2: expanded discussion on constraints in
section 7, matches published versio
Localization of Eigenfunctions in the Stadium Billiard
We present a systematic survey of scarring and symmetry effects in the
stadium billiard. The localization of individual eigenfunctions in Husimi phase
space is studied first, and it is demonstrated that on average there is more
localization than can be accounted for on the basis of random-matrix theory,
even after removal of bouncing-ball states and visible scars. A major point of
the paper is that symmetry considerations, including parity and time-reversal
symmetries, enter to influence the total amount of localization. The properties
of the local density of states spectrum are also investigated, as a function of
phase space location. Aside from the bouncing-ball region of phase space,
excess localization of the spectrum is found on short periodic orbits and along
certain symmetry-related lines; the origin of all these sources of localization
is discussed quantitatively and comparison is made with analytical predictions.
Scarring is observed to be present in all the energy ranges considered. In
light of these results the excess localization in individual eigenstates is
interpreted as being primarily due to symmetry effects; another source of
excess localization, scarring by multiple unstable periodic orbits, is smaller
by a factor of .Comment: 31 pages, including 10 figure
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