2,955 research outputs found
Nucleation scaling in jigsaw percolation
Jigsaw percolation is a nonlocal process that iteratively merges connected
clusters in a deterministic "puzzle graph" by using connectivity properties of
a random "people graph" on the same set of vertices. We presume the
Erdos--Renyi people graph with edge probability p and investigate the
probability that the puzzle is solved, that is, that the process eventually
produces a single cluster. In some generality, for puzzle graphs with N
vertices of degrees about D (in the appropriate sense), this probability is
close to 1 or small depending on whether pD(log N) is large or small. The one
dimensional ring and two dimensional torus puzzles are studied in more detail
and in many cases the exact scaling of the critical probability is obtained.
The paper settles several conjectures posed by Brummitt, Chatterjee, Dey, and
Sivakoff who introduced this model.Comment: 39 pages, 3 figures. Moved main results to the introduction and
improved exposition of section
Is the proton radius puzzle evidence of extra dimensions?
The proton charge radius inferred from muonic hydrogen spectroscopy is not
compatible with the previous value given by CODATA-2010, which, on its turn,
essentially relies on measurements of the electron-proton interaction. The
proton's new size was extracted from the 2S-2P Lamb shift in the muonic
hydrogen, which showed an energy excess of 0.3 meV in comparison to the
theoretical prediction, evaluated with the CODATA radius. Higher-dimensional
gravity is a candidate to explain this discrepancy, since the muon-proton
gravitational interaction is stronger than the electron-proton interaction and,
in the context of braneworld models, the gravitational potential can be hugely
amplified in short distances when compared to the Newtonian potential.
Motivated by these ideas, we study a muonic hydrogen confined in a thick brane.
We show that the muon-proton gravitational interaction modified by extra
dimensions can provide the additional separation of 0.3 meV between 2S and 2P
states. In this scenario, the gravitational energy depends on the
higher-dimensional Planck mass and indirectly on the brane thickness. Studying
the behavior of the gravitational energy with respect to the brane thickness in
a realistic range, we find constraints for the fundamental Planck mass that
solve the proton radius puzzle and are consistent with previous experimental
bounds.Comment: Updated with new dat
The Torus Operator in Holography
We consider the non-local operator defined in 2-dimensional
CFTs by the path integral over a torus with two punctures. Using the AdS/CFT
correspondence, we study the spectrum and ground state of this operator in
holographic such CFTs in the limit of large central charge . In one region
of moduli space, we argue that the operator retains a finite gap and has a
ground state that differs from the CFT vacuum only by order one corrections. In
this region the torus operator is much like the cylinder operator. But in
another region of moduli space we find a puzzle. Although our is
of the manifestly positive form , studying the most tractable
phases of suggests that has
negative eigenvalues. It seems clear that additional phases must become
relevant at large , perhaps leading to novel behavior associated with a
radically different ground state or a much higher density of states. By
studying the action of two such torus operators on the CFT ground state, we
also provide evidence that, even at large , the relevant bulk saddles have
surfaces with small genus.Comment: 42 pages, 24 figures, introduction rewritten for clarity, appendix
adde
Cosmological constant, violation of cosmological isotropy and CMB
We suggest that the solution to the cosmological vacuum energy puzzle does
not require any new field beyond the standard model, but rather can be
explained as a result of the interaction of the infrared sector of the
effective theory of gravity with standard model fields. The cosmological
constant in this framework can be presented in terms of QCD parameters and the
Hubble constant as follows, \epsilon_{vac} \sim H \cdot m_q\la\bar{q}q\ra
/m_{\eta'} \sim (4.3\cdot 10^{-3} \text{eV})^4, which is amazingly close to
the observed value today. In this work we explain how this proposal can be
tested by analyzing CMB data. In particular, knowing the value of the observed
cosmological constant fixes univocally the smallest size of the spatially flat,
constant time 3d hypersurface which, for instance in the case of an effective
1-torus, is predicted to be around 74 Gpc. We also comment on another important
prediction of this framework which is a violation of cosmological isotropy.
Such anisotropy is indeed apparently observed by WMAP, and will be confirmed
(or ruled out) by future PLANCK data.Comment: uses revtex4 - v2 as publishe
Chern-Simons Gauge Theory and the AdS(3)/CFT(2) Correspondence
The bulk partition function of pure Chern-Simons theory on a three-manifold
is a state in the space of conformal blocks of the dual boundary RCFT, and
therefore transforms non-trivially under the boundary modular group. In
contrast the bulk partition function of AdS(3) string theory is the
modular-invariant partition function of the dual CFT on the boundary. This is a
puzzle because AdS(3) string theory formally reduces to pure Chern-Simons
theory at long distances. We study this puzzle in the context of massive
Chern-Simons theory. We show that the puzzle is resolved in this context by the
appearance of a chiral "spectator boson" in the boundary CFT which restores
modular invariance. It couples to the conformal metric but not to the gauge
field on the boundary. Consequently, we find a generalization of the standard
Chern-Simons/RCFT correspondence involving "nonholomorphic conformal blocks"
and nonrational boundary CFTs. These generalizations appear in the
long-distance limit of AdS(3) string theory, where the role of the spectator
boson is played by other degrees of freedom in the theory.Comment: 43 pages, harvma
Dust reverberation-mapping of the Seyfert 1 galaxy WPVS48
Using robotic telescopes of the Universitatssternwarte Bochum near Cerro
Armazones in Chile, we monitored the z=0.0377 Seyfert 1 galaxy WPVS48 (2MASX
J09594263-3112581) in the optical (B and R) and near-infrared (NIR, J and Ks)
with a cadence of two days. The light curves show unprecedented variability
details. The NIR variation features of WPVS48 are consistent with the
corresponding optical variations, but the features appear sharper in the NIR
than in the optical, suggesting that the optical photons undergo multiple
scatterings. The J and Ks emission, tracing the hot (1600 K) dust echo, lags
the B and R variations by on average 64 +/- 4 days and 71 +/- 5 days,
respectively (restframe). WPVS48 lies on the known tau-M_V relationship.
However, the observed lag is about three times shorter than expected from the
dust sublimation radius r_sub inferred from the optical-UV luminosity, and
explanations for this common discrepancy are searched for. The sharp NIR echos
argue for a face-on torus geometry and allow us to put forward two potential
scenarios: 1) as previously proposed, in the equatorial plane of the accretion
disk the inner region of the torus is flattened and may come closer to the
accretion disk. 2) The dust torus with inner radius r_sub is geometrically and
optically thick, so that the observer only sees the facing rim of the torus
wall, which lies closer to the observer than the torus equatorial plane and
therefore leads to an observed foreshortened lag. Both scenarios are able to
explain the factor three discrepancy between tau and r_sub. Longer-wavelength
dust reverberation data might enable one to distinguish between the scenarios.Comment: 4 pages, 6 figures, Published in Astronomy and Astrophysic
Can Black Hole Relax Unitarily?
We review the way the BTZ black hole relaxes back to thermal equilibrium
after a small perturbation and how it is seen in the boundary (finite volume)
CFT. The unitarity requires the relaxation to be quasi-periodic. It is
preserved in the CFT but is not obvious in the case of the semiclassical black
hole the relaxation of which is driven by complex quasi-normal modes. We
discuss two ways of modifying the semiclassical black hole geometry to maintain
unitarity: the (fractal) brick wall and the worm-hole modification. In the
latter case the entropy comes out correctly as well.Comment: 12 pages, Based on talks given at ``Black Holes IV'', Honey Harbour,
June 2003 and at BW2003, Vrnjacka Banja, August 200
- …