286 research outputs found
Dimensional Reduction via Noncommutative Spacetime: Bootstrap and Holography
Unlike noncommutative space, when space and time are noncommutative, it seems
necessary to modify the usual scheme of quantum mechanics. We propose in this
paper a simple generalization of the time evolution equation in quantum
mechanics to incorporate the feature of a noncommutative spacetime. This
equation is much more constraining than the usual Schr\"odinger equation in
that the spatial dimension noncommuting with time is effectively reduced to a
point in low energy. We thus call the new evolution equation the spacetime
bootstrap equation, the dimensional reduction called for by this evolution
seems close to what is required by the holographic principle. We will discuss
several examples to demonstrate this point.Comment: 15 pages, harvmac. v2: typos corrected and some changes mad
CMB Power Spectrum from Noncommutative Spacetime
Very recent CMB data of WMAP offers an opportunity to test inflation models,
in particular, the running of spectral index is quite new and can be used to
rule out some models. We show that an noncommutative spacetime inflation model
gives a good explanation of these new results. In fitting the data, we also
obtain a relationship between the noncommutative parameter (string scale) and
the ending time of inflation.Comment: 8 pages, 2 figures; v2: refs. added and minor corrections; v3:
further minor correctio
Fuzzy Gravitons From Uncertain Spacetime
The recently proposed remarkable mechanism explaining ``stringy exclusion
principle" on an Anti de Sitter space is shown to be another beautiful
manifestation of spacetime uncertainty principle in string theory as well as in
M theory. Put in another way, once it is realized that the graviton of a given
angular momentum is represented by a spherical brane, we deduce the maximal
angular momentum directly from either the relation
in M theory or \Delta t\Delta x>\ap in string theory. We also show that the
result of hep-th/0003075 is similar to results on D2-branes in SU(2) WZW model.
Using the dual D2-brane representation of a membrane, we obtain the
quantization condition for the size of the membrane.Comment: 10 pages, harvmac. v2: a ref. and a note added; v3: A remark and one
more ref. adde
Rapid Brain Responses to Familiar vs. Unfamiliar Music – an EEG and Pupillometry study
Human listeners exhibit marked sensitivity to familiar music, perhaps most readily revealed by popular “name that tune” games, in which listeners often succeed in recognizing a familiar song based on extremely brief presentation. In this work, we used electroencephalography (EEG) and pupillometry to reveal the temporal signatures of the brain processes that allow differentiation between a familiar, well liked, and unfamiliar piece of music. In contrast to previous work, which has quantified gradual changes in pupil diameter (the so-called “pupil dilation response”), here we focus on the occurrence of pupil dilation events. This approach is substantially more sensitive in the temporal domain and allowed us to tap early activity with the putative salience network. Participants (N = 10) passively listened to snippets (750 ms) of a familiar, personally relevant and, an acoustically matched, unfamiliar song, presented in random order. A group of control participants (N = 12), who were unfamiliar with all of the songs, was also tested. We reveal a rapid differentiation between snippets from familiar and unfamiliar songs: Pupil responses showed greater dilation rate to familiar music from 100–300 ms post-stimulus-onset, consistent with a faster activation of the autonomic salience network. Brain responses measured with EEG showed a later differentiation between familiar and unfamiliar music from 350 ms post onset. Remarkably, the cluster pattern identified in the EEG response is very similar to that commonly found in the classic old/new memory retrieval paradigms, suggesting that the recognition of brief, randomly presented, music snippets, draws on similar processes
Casimir Energy of the Universe and New Regularization of Higher Dimensional Quantum Field Theories
Casimir energy is calculated for the 5D electromagnetism and 5D scalar theory
in the {\it warped} geometry. It is compared with the flat case. A new
regularization, called {\it sphere lattice regularization}, is taken. In the
integration over the 5D space, we introduce two boundary curves (IR-surface and
UV-surface) based on the {\it minimal area principle}. It is a {\it direct}
realization of the geometrical approach to the {\it renormalization group}. The
regularized configuration is {\it closed-string like}. We do {\it not} take the
KK-expansion approach. Instead, the position/momentum propagator is exploited,
combined with the {\it heat-kernel method}. All expressions are closed-form
(not KK-expanded form). The {\it generalized} P/M propagators are introduced.
We numerically evaluate \La(4D UV-cutoff), \om(5D bulk curvature, warp
parameter) and (extra space IR parameter) dependence of the Casimir energy.
We present two {\it new ideas} in order to define the 5D QFT: 1) the summation
(integral) region over the 5D space is {\it restricted} by two minimal surfaces
(IR-surface, UV-surface) ; or 2) we introduce a {\it weight function} and
require the dominant contribution, in the summation, is given by the {\it
minimal surface}. Based on these, 5D Casimir energy is {\it finitely} obtained
after the {\it proper renormalization procedure.} The {\it warp parameter}
\om suffers from the {\it renormalization effect}. The IR parameter does
not. We examine the meaning of the weight function and finally reach a {\it new
definition} of the Casimir energy where {\it the 4D momenta(or coordinates) are
quantized} with the extra coordinate as the Euclidean time (inverse
temperature). We examine the cosmological constant problem and present an
answer at the end. Dirac's large number naturally appears.Comment: 13 paes, 8 figures, proceedings of 1st Mediterranean Conf. on CQ
On the Bekenstein-Hawking Entropy, Non-Commutative Branes and Logarithmic Corrections
We extend earlier work on the origin of the Bekenstein-Hawking entropy to
higher-dimensional spacetimes. The mechanism of counting states is shown to
work for all spacetimes associated with a Euclidean doublet
of electric-magnetic dual brane pairs of type II
string-theory or M-theory wrapping the spacetime's event horizon plus the
complete internal compactification space. Non-Commutativity on the brane
worldvolume enters the derivation of the Bekenstein-Hawking entropy in a
natural way. Moreover, a logarithmic entropy correction with prefactor 1/2 is
derived.Comment: 17 pages, 2 figures; refs. adde
Modeling M-Theory Vacua via Gauged S-Duality
We construct a model of M-theory vacua using gauged S-duality and the
Chan-Paton symmetries by introducing an infinite number of open string charges.
In the Bechi-Rouet-Stora-Tyutin formalism, the local description of the gauged
S-duality on its moduli space of vacua is fully determined by one physical
state condition on the vacua. We introduce the string probe of the spatial
degrees of freedom and define the increment of the cosmic time. The
dimensionality of space-time and the gauge group of the low energy effective
theory originate in the symmetries (with or without their breakdown) in our
model. This modeling leads to the derived category formulation of the quantum
mechanical world including gravity and to the concept of a non-linear potential
of gauged and affinized S-duality which specifies the morphism structure of
this derived category.Comment: 31 pages, version reflecting the erratum. arXiv admin note:
substantial text overlap with arXiv:1102.460
Noncommutative models in patch cosmology
We consider several classes of noncommutative inflationary models within an
extended version of patch cosmological braneworlds, starting from a maximally
invariant generalization of the action for scalar and tensor perturbations to a
noncommutative brane embedded in a commutative bulk. Slow-roll expressions and
consistency relations for the cosmological observables are provided, both in
the UV and IR region of the spectrum; the inflaton field is assumed to be
either an ordinary scalar field or a Born-Infeld tachyon. The effects of
noncommutativity are then analyzed in a number of ways and energy regimes.Comment: 13 pages, 8 figures. Figures 1 and 2 are included in the text, Figs.
3-8 are in a low-resolution jpeg format. These and other high-resolution
figures are available upon request to the author ([email protected]). v3:
corrected misprint
On the Zero-Slope Limit of the Compactified Closed Bosonic String
In the framework of the compactified closed bosonic string theory with the
extra spatial coordinates being circular with radius , we perform both the
zero-slope limit and the limit of the tree scattering
amplitude of four massless scalar particles. We explicitly show that this
double limit leads to amplitudes involving scalars which interact through the
exchange of a scalar, spin 1 and spin 2 particle. In particular, this latter
case reproduces the same result obtained in linearized quantum gravity.Comment: 10 pages, LaTex file, DSF-T-43/9
Proposal of a topological M(atrix) theory
Keeping in mind the several models of M(atrix) theory we attempt to
understand the possible structure of the topological M(atrix) theory
``underlying'' these approaches. In particular we are motivated by the issue
about the nature of the structure of the vacuum of the topological M(atrix)
theory and how this could be related to the vacuum of the electroweak theory.
In doing so we are led to a simple topological matrix model. Moreover it is
intuitively expected from the current understanding that the noncommutative
nature of ``spacetime'' and background independence should lead to a
topological Model. The main purpose of this note is to propose a simple
topological Matrix Model which bears relation to F and M theories. Suggestions
on the origin of the chemical potential term appearing in the matrix models are
given.Comment: 14 pages revte
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