Partial Deconfinement in Color Superconductivity

We analyze the fate of the unbroken SU(2) color gauge interactions for 2 light flavors color superconductivity at non zero temperature. Using a simple model we compute the deconfining/confining critical temperature and show that is smaller than the critical temperature for the onset of the superconductive state itself. The breaking of Lorentz invariance, induced already at zero temperature by the quark chemical potential, is shown to heavily affect the value of the critical temperature and all of the relevant features related to the deconfining transition. Modifying the Polyakov loop model to describe the SU(2) immersed in the diquark medium we argue that the deconfinement transition is second order. Having constructed part of the equation of state for the 2 color superconducting phase at low temperatures our results are relevant for the physics of compact objects featuring a two flavor color superconductive state.Comment: 9 pp, 4 eps-figs, version to appear in PR

DCC dynamics with the SU(3) linear sigma model

The SU(3) extension of the linear sigma model is employed to elucidate the effect of including strangeness on the formation of disoriented chiral condensates. By means of a Hartree factorization, approximate dispersion relations for the 18 scalar and pseudoscalar meson species are derived and their self-consistent solution makes it possible to trace out the thermal path of the two order parameters as well as delineate the region of instability within which spontaneous pair creation becomes possible. The results depend significantly on the employed sigma mass, with the highest values yielding the largest regions of instability. An approximate solution of the equations of motion for the order parameter in scenarios emulating uniform scaling expansions show that even with a rapid quench only the pionic modes grow unstable. Nevertheless, the rapid and oscillatory relaxation of the order parameters leads to enhanced production of both pions and (to a lesser degree) kaons.Comment: 29 pages, RevTeX, 11 postscript figures, discussion about anomaly term adde

Spontaneous CP Violating Phase as the Phase in PMNS Matrix

We study the possibility of identifying the CP violating phases in the PMNS mixing matrix in the lepton sector and also that in the CKM mixing matrix in the quark sector with the phase responsible for the spontaneous CP violation in the Higgs potential, and some implications. Since the phase in the CKM mixing matrix is determined by experimental data, the phase in the lepton sector is therefore also fixed. The mass matrix for neutrinos is constrained leading to constraints on the Jarlskog CP violating parameter $J$, and the effective mass $$ for neutrinoless double beta decay. The Yukawa couplings are also constrained. Different ways of identifying the phases have different predictions for $\mu \to e e\bar e$ and $\tau \to l_1 l_2 \bar l_3$. Future experimental data can be used to distinguish different models.Comment: 16 pages, 3 figure

Chiral symmetry restoration in linear sigma models with different numbers of quark flavors

Chiral symmetry restoration at nonzero temperature is studied in the framework of the O(4) linear sigma model and the U(N_f)_r x U(N_f)_l linear sigma model with N_f=2,3, and 4 quark flavors. We investigate the temperature dependence of the masses of the scalar and pseudoscalar mesons, and the non-strange, strange, and charm condensates within the Hartree approximation as derived from the Cornwall-Jackiw-Tomboulis formalism. We find that the masses of the non-strange and strange mesons at nonzero temperature depend sensitively on the particular symmetry of the model and the number of light quark flavors N_f. On the other hand, due to the large charm quark mass, neither do charmed mesons significantly affect the properties of the other mesons, nor do their masses change appreciably in the temperature range around the chiral symmetry restoration temperature. In the chiral limit, the transition temperatures for chiral symmetry restoration are surprisingly close to those found in lattice QCD.Comment: 28 pages, 8 figure

Linking the chiral and deconfinement phase transitions

We show that the electric glueball becomes critical at the end-point of the deconfinement phase transition in finite temperature QCD. Based on this observation and existing lattice data, we argue that the chiral phase transition at a zero quark mass and the deconfinement phase transition at an infinite quark mass are continuously connected by the glueball-sigma mixing.Comment: 4 pages, terminology corrected. To appear in Phys. Rev.

Can filesharers be triggered by economic incentives? Results of an experiment

Illegal filesharing on the internet leads to considerable financial losses for artists and copyright owners as well as producers and sellers of music. Thus far, measures to contain this phenomenon have been rather restrictive. However, there are still a considerable number of illegal systems, and users are able to decide quite freely between legal and illegal downloads because the latter are still difficult to sanction. Recent economic approaches account for the improved bargaining position of users. They are based on the idea of revenue-splitting between professional sellers and peers. In order to test such an innovative business model, the study reported in this article carried out an experiment with 100 undergraduate students, forming five small peer-to-peer networks.The networks were confronted with different economic conditions.The results indicate that even experienced filesharers hold favourable attitudes towards revenue-splitting.They seem to be willing to adjust their behaviour to different economic conditions

Low Energy Theory for 2 flavors at High Density QCD

We construct the effective Lagrangian describing the low energy excitations for Quantum Chromodynamics with two flavors at high density. The non-linear realization framework is employed to properly construct the low energy effective theory. The light degrees of freedom, as required by 't Hooft anomaly conditions, contain massless fermions which we properly include in the effective Lagrangian. We also provide a discussion of the linearly realized Lagrangian.Comment: 17 pages, RevTeX format, references added. To appear in Phys. Rev.

The Superfluid and Conformal Phase Transitions of Two-Color QCD

The phase structure of two-color QCD is examined as a function of the chemical potential and the number of light quark flavors. We consider effective Lagrangians for two-color QCD containing the Goldstone excitations, spin-one particles and negative intrinsic parity terms. We discuss the possibility of a conformal phase transition and the enhancement of the global symmetries as the number of flavors is increased. The effects of a quark chemical potential on the spin-one particles and on the negative intrinsic parity terms are analyzed. It is shown that the phase diagram that is predicted by the linearly realized effective Lagrangian at tree-level matches exactly that predicted by chiral perturbation theory.Comment: ReVTeX, 23 pages, 3 figures. Discussion of vector condensation extended, two figures added, references adde

Mathematics of Gravitational Lensing: Multiple Imaging and Magnification

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an asymptotic expression for the global expected number of micro-minima. Multiple imaging in optical geometry and a spacetime setting are treated. We review global magnification relation results for model-dependent scenarios and cover recent developments on universal local magnification relations for higher order caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of General Relativity and Gravitatio

Stability of Black Holes and Black Branes

We establish a new criterion for the dynamical stability of black holes in $D \geq 4$ spacetime dimensions in general relativity with respect to axisymmetric perturbations: Dynamical stability is equivalent to the positivity of the canonical energy, \E, on a subspace, $\mathcal T$, of linearized solutions that have vanishing linearized ADM mass, momentum, and angular momentum at infinity and satisfy certain gauge conditions at the horizon. This is shown by proving that---apart from pure gauge perturbations and perturbations towards other stationary black holes---\E is nondegenerate on $\mathcal T$ and that, for axisymmetric perturbations, \E has positive flux properties at both infinity and the horizon. We further show that \E is related to the second order variations of mass, angular momentum, and horizon area by \E = \delta^2 M - \sum_A \Omega_A \delta^2 J_A - \frac{\kappa}{8\pi} \delta^2 A, thereby establishing a close connection between dynamical stability and thermodynamic stability. Thermodynamic instability of a family of black holes need not imply dynamical instability because the perturbations towards other members of the family will not, in general, have vanishing linearized ADM mass and/or angular momentum. However, we prove that for any black brane corresponding to a thermodynamically unstable black hole, sufficiently long wavelength perturbations can be found with \E < 0 and vanishing linearized ADM quantities. Thus, all black branes corresponding to thermodynmically unstable black holes are dynamically unstable, as conjectured by Gubser and Mitra. We also prove that positivity of \E on $\mathcal T$ is equivalent to the satisfaction of a "local Penrose inequality," thus showing that satisfaction of this local Penrose inequality is necessary and sufficient for dynamical stability.Comment: 54 pages, Latex, 2 figures, v2: Anzatz for momentum in proof of Gubser-Mitra conjecture corrected; factor of 2 in symplectic form corrected; several typos in formulas corrected; v3: revised argument concerning horizon gauge condition on p. 10; typos corrected and several minor changes; reference added; v4: formula (86) for \E corrected, footnote adde