The Brownian motion of a charged test particle caused by quantum electromagnetic vacuum fluctuations between two perfectly conducting plates is examined and the mean squared fluctuations in the velocity and position of the test particle are calculated. Our results show that the Brownian motion in the direction normal to the plates is reinforced in comparison to that in the single plate case. The effective temperature associated with this normal Brownian motion could be three times as large as that in the single plate case. However, the negative dispersions for the velocity and position in the longitudinal directions, which could be interpreted as reducing the quantum uncertainties of the particle, acquire positive corrections due to the presence of the second plate, and are thus weakened.

We systematically construct wave functions and vertex operators in the type IIB (IKKT) matrix model by expanding a supersymmetric Wilson loop operator. They form a massless multiplet of the $\mathcal{N}=2$ type IIB supergravity and automatically satisfy conservation laws.

We explicitly derive, following a Noether-like approach, the criteria for preserving Poincaré invariance in noncommutative gauge theories. Using these criteria we discuss the various spacetime symmetries in such theories. It is shown that, interpreted appropriately, Poincaré invariance holds. The analysis is performed in both the commutative as well as noncommutative descriptions and a compatibility between the two is also established.

It has long been known that matter charged under a broken U(1) gauge symmetry collapsing to form a black hole will radiate away the associated external (massive) gauge field. We show that the time scale for the radiation of the monopole component of the field will be on the order of the inverse Compton wavelength of the gauge boson (assuming natural units). Since the Compton wavelength for a massive gauge boson is directly related to the scale of symmetry breaking, the time scale for a black hole to lose its gauge field “hair” is determined only by this scale. The time scale for Hawking radiation, however, is set by the mass of the black hole. These different dependencies mean that for any (sub-Planckian) scale of symmetry breaking we can define a mass below which black holes radiate quickly enough to discharge themselves via the Hawking process before the gauge field is radiated away. This has important implications for the extrapolation of classical black hole physics to Planck-scale virtual black holes. In particular, we comment on the implications for protecting protons from gravitationally mediated decay.

Motivated in part by string theory, we consider a modification of the $\Lambda \mathrm{C}\mathrm{D}\mathrm{M}$ cosmological model in which the dark matter has a long-range scalar force screened by light particles. Scalar forces can have interesting effects on structure formation: the main example presented here is the expulsion of dark matter halos from low density regions, or voids, in the galaxy distribution.

Motivated in part by string theory, we consider the idea that the standard $\Lambda \mathrm{C}\mathrm{D}\mathrm{M}$ cosmological model might be modified by the effect of a long-range scalar dark matter interaction. The variant of this widely-discussed notion considered here is suggested by the Brandenberger-Vafa [R. H. Brandenberger and C. Vafa, Nucl. Phys. B316, 391 (1989).] picture for why we perceive three spatial dimensions. In this picture there may be at least two species of dark matter particles, with scalar charges such that the scalar interaction attracts particles with like sign and repels unlike signs. The net charge vanishes. Under this condition the evolution of the mass distribution in linear perturbation theory is the same as in the $\Lambda \mathrm{C}\mathrm{D}\mathrm{M}$ cosmology, and both models therefore can equally well pass the available cosmological tests. The physics can be very different on small scales, however: if the scalar interaction has the strength suggested by simple versions of the string scenario, nonlinear mass concentrations are unstable against separation into charged halos with properties unlike the standard model prediction and possibly of observational interest.

A detailed numerical and analytical examination of the evolution of stochastic magnetic fields between a putative magnetogenesis era at high cosmic temperatures $T\sim 100\mathrm{M}\mathrm{e}\mathrm{V}–100\mathrm{G}\mathrm{e}\mathrm{V}$ and the present epoch is presented. The analysis includes all relevant dissipation processes, such as neutrino- and photon-induced fluid viscosities as well as ambipolar and hydrogen diffusion. A simple and intuitive analytical model matching the results of the three-dimensional MHD simulations allows for the prediction of prerecombination and present day magnetic field correlation lengths and energy densities as a function of initial magnetic field energy density, helicity, and spectral index. Our conclusions are multifold. (a) Initial primordial fields with only a small amount of helicity are evolving into maximally helical fields at the present. Furthermore, the simulations show a self-similarity in the evolution of maximally helical fields implying a seemingly acausual amplification of magnetic fields on large scales is observed. (b) There exists a correlation between the strength of the magnetic field $B$ at the peak of its spectrum and the location of the peak, given at the present epoch by $B\approx 5\times {10}^{-12}\mathrm{G}(L/\mathrm{k}\mathrm{p}\mathrm{c})$, where $L$ is the magnetic field correlation length determined by the initial properties of the magnetic field. (c) Concerning studies of the generation of cosmic microwave background (CMBR) anisotropies due to primordial magnetic fields of $B\sim {10}^{-9}\mathrm{G}$ on $\gtrsim 10\mathrm{M}\mathrm{p}\mathrm{c}$ scales, such fields are not only impossible to generate in early causal magnetogenesis scenarios but also seemingly ruled out by distortions of the CMBR spectrum due to magnetic field dissipation on smaller scales and the overproduction of cluster-magnetic fields. (d) The most promising detection possibility of CMBR distortions due to primordial magnetic fields may be on much smaller scales at higher multipoles $l\sim {10}^6$ where the signal is predicted to be the strongest. (e) It seems possible that magnetic fields in clusters of galaxies are entirely of primordial origin, without invoking dynamo amplification. Such fields would be of (precollapse) strength ${10}^{-12}–{10}^{-11}\mathrm{G}$ with correlation lengths in the kpc range and would also exist in voids of galaxies.

The integrated Sachs-Wolfe effect in the cosmic microwave background as measured through its correlation with galaxies provides a unique opportunity to study the dynamics of the dark energy through its large scale clustering properties. Ultimately, a deep all-sky galaxy survey out to $z\sim 2$ can make a $\sim 10\sigma$ or $\sim 10\%$ measurement of the correlation and limit $\sim 3\%$ changes in the gravitational potential or total density fluctuation due to dark energy clustering on the Gpc scale. A canonical single scalar field or quintessence model predicts that these clustering effects will appear on the horizon scale with a strength that reflects the evolution of the dark energy density. In terms of a constant equation of state, this would allow tests of the quintessence prediction for models where $|1+w|\gtrsim 0.05$.

Nonlinear interactions among the inertial modes of a rotating fluid can be described by a network of coupled oscillators. We use such a description for an incompressible fluid to study the development of the r-mode instability of rotating neutron stars. A previous hydrodynamical simulation of the r-mode reported the catastrophic decay of large amplitude r-modes. We explain the dynamics and timescale of this decay analytically by means of a single three mode coupling. We argue that at realistic driving and damping rates such large amplitudes will never actually be reached. By numerically integrating a network of nearly 5000 coupled modes, we find that the linear growth of the r-mode ceases before it reaches an amplitude of around ${10}^{-4}$. The lowest parametric instability thresholds for the r-mode are calculated and it is found that the r-mode becomes unstable to modes with $13<n<15$ if modes up to $n=30$ are included. Using the network of coupled oscillators, integration times of ${10}^6$ rotational periods are attainable for realistic values of driving and damping rates. Complicated dynamics of the modal amplitudes are observed. The initial development is governed by the three mode coupling with the lowest parametric instability. Subsequently, a large number of modes are excited, which greatly decreases the linear growth rate of the r-mode.

We continue our exploration of the collective modes of an anisotropic quark-gluon plasma by extending our previous analysis to arbitrary Riemann sheets. We demonstrate that in the presence of momentum-space anisotropies in the parton distribution functions there are new relevant singularities on the neighboring unphysical sheets. We then show that for sufficiently strong anisotropies that these singularities move into the region of spacelike momentum and their effect can extend down to the physical sheet. In order to demonstrate this explicitly we consider the polarization tensor for gluons propagating parallel to the anisotropy direction. We derive analytic expressions for the gluon structure functions in this case and then analytically continue them to unphysical Riemann sheets. Using the resulting analytic continuations we numerically determine the position of the unphysical singularities. We then show that in the limit of infinite contraction of the distribution function along the anisotropy direction that the unphysical singularities move onto the physical sheet and result in real spacelike modes at large momenta for all “out-of-plane” angles of propagation.

The dilepton production is investigated in proton-nucleus collisions in the forward region using the Color Glass Condensate approach. The transverse momentum distribution ($p_T$), more precisely the low $p_T$ region, where the saturation effects are expected to increase, is analyzed. The ratio between proton-nucleus and proton-proton differential cross section for RHIC and LHC energies is evaluated, showing the effects of saturation at small $p_T$, and presenting a suppression of the Cronin type peak at moderate $p_T$. These features indicate the dilepton as a most suitable probe to study the properties of the saturated regime and the Cronin effect.

The excess of cosmic positrons observed by the High-Energy Antimatter Telescope (HEAT) experiment may be the result of Kaluza-Klein dark matter annihilating in the galactic halo. Kaluza-Klein dark matter annihilates dominantly into charged leptons that yield a large number and hard spectrum of positrons per annihilation. Given a Kaluza-Klein dark matter particle with a mass in the range of 300 GeV–400 GeV, no exceptional substructure or clumping is needed in the local distribution of dark matter to generate a positron flux that explains the HEAT observations. This is in contrast to supersymmetric dark matter which requires unnaturally large amounts of dark substructure to produce the observed positron excess. Future astrophysical and collider tests are outlined that will confirm or rule out this explanation of the HEAT data.

The assumption of strong diquark correlations in the QCD spectrum suggests flavor multiplets of hadrons that are degenerate in the chiral limit. Generally it would be unnatural for there to be degeneracy in the hadron spectrum that is not protected by a QCD symmetry. Here we show—for pentaquarks constructed from diquarks—that these degeneracies can be naturally protected by the full chiral symmetry of QCD. The resulting chiral multiplet structure recovers the ideally mixed pentaquark mass spectrum of the diquark model, and interestingly, requires that the axial couplings of the pentaquarks to states outside the degenerate multiplets vanish in the chiral limit. This result suggests that if these hadrons exist, they are stable in the chiral limit and therefore have widths that scale as the fourth power of the kaon mass over the chiral-symmetry breaking scale. Natural-size widths are of order a few MeV.

We present a model for next-to-leading order resummed threshold form factors based on a timelike coupling recently introduced in the framework of small $x$ physics. Improved expressions for the form factors in $N$-space are obtained which are not plagued by Landau-pole singularities, as the included absorptive effects—usually neglected—act as regulators. The physical reason is that, because of faster decay of gluon jets, there is not enough resolution time to observe the Landau pole. Our form factors reduce to the standard ones when the absorptive parts related to the coupling are neglected. The inverse transform from $N$-space to $x$-space can be done directly without any prescription and we obtain analytical expressions for the form factors, which are well defined in all $x$-space.

Using the CLEO detector at the Cornell Electron-positron Storage Ring, we have measured the scaled momentum spectra, $d\sigma /d{x}_p$, and the inclusive production cross sections of the charm mesons $D^{+}$, $D^0$, $D^{\star +}$, and $D^{\star 0}$ in $e^{+}{e}^{-}$ annihilation at about 10.5 GeV center of mass energy, excluding the decay products of $B$ mesons. The statistical accuracy and momentum resolution are superior to previous measurements at this energy.

I discuss the range of validity of Detweiler’s formula for the resonant frequencies of rapidly rotating Kerr black holes. While his formula is correct for extremal black holes, it has also been commonly accepted that it describes very well the resonant frequencies of near extremal black holes, and that therefore there is a large number of modes clustering on the real axis as the black hole becomes extremal. I will show that this last statement is not only incorrect, but that it also does not follow from Detweiler’s formula, provided it is handled with due care. It turns out that only the first $n\ll -\log (r_{+}-r_{-})/r_{+}$ modes are well described by that formula, which translates, for any astrophysical black hole, into one or two modes only. All existing numerical data give further support to this claim. I also discuss some implications of this result for recent investigations on the late-time dynamics of rapidly rotating black holes.

Quantum energy inequalities (QEIs) were established by Flanagan for the massless scalar field on two-dimensional Lorentzian spacetimes globally conformal to Minkowski space. We extend his result to all two-dimensional globally hyperbolic Lorentzian spacetimes and use it to show that flat spacetime QEIs give a good approximation to the curved spacetime results on sampling time scales short in comparison with natural geometric scales. This is relevant to the application of QEIs to constrain exotic spacetime metrics.