We investigate the phase portrait of the ($1+1$)-dimensional massless two-flavored ${\mathrm{NJL}}_2$ model containing a quark number chemical potential $\mu$ and an isospin chemical potential ${\mu }_I$ in the limit of a large number of colors $N_c\to \infty$. Particular attention is paid to the question of to what extent the inclusion of an isospin asymmetry affects chiral condensates to have a spatial inhomogeneity in the form of the so-called chiral density waves (CDW) (chiral spirals). It is shown that, at zero temperature and comparatively small values of $\mu$, i.e. at $\mu <{\mu }_c\approx 0.68M_0$ ($M_0$ is the dynamical quark mass in the vacuum), only the homogeneous charged pion condensation phase is realized for arbitrary nonzero values of ${\mu }_I$. Contrary to this, for large values of $\mu >{\mu }_c$, two CDW phases appear in the $({\mu }_I,\mu )$-phase diagram of the model. In the first phase, CDWs are clockwise twisted chiral spirals, and in the second phase they are counterclockwise. The influence of nonzero temperature on the formation of the CDW phases is also investigated.

We formulate quantum mechanics on the group $SO(3)$ using a noncommutative dual space representation for the quantum states, inspired by recent work in quantum gravity. The new noncommutative variables have a clear connection to the corresponding classical variables, and our analysis confirms them as the natural phase space variables, both mathematically and physically. In particular, we derive the first order (Hamiltonian) path integral in terms of the noncommutative variables, as a formulation of the transition amplitudes alternative to that based on harmonic analysis. We find that the nontrivial phase space structure gives naturally rise to quantum corrections to the action for which we find a closed expression. We then study both the semiclassical approximation of the first order path integral and the example of a free particle on $SO(3)$. On the basis of these results, we comment on the relevance of similar structures and methods for more complicated theories with group-based configuration spaces, such as loop quantum gravity and spin foam models.

The usual description of self-induced neutrino flavor conversions in core-collapse supernovae is based on the dominance of the neutrino density $n_{\nu }$ over the net electron density $n_e$. However, this condition is not met during the post-bounce accretion phase, when the dense matter in a SN is piled up above the neutrinosphere. As recently pointed out, a dominant matter term in the anisotropic SN environment would dephase the flavor evolution for neutrinos traveling on different trajectories, challenging the occurrence of the collective behavior in the dense neutrino gas. Using the results from recent long-term simulations of core-collapse SN explosions, based on three-flavor Boltzmann neutrino transport in spherical symmetry, we find that both the situations of complete matter suppression (when $n_e\gg n_{\nu }$) and matter-induced decoherence (when $n_e\gtrsim n_{\nu }$) of flavor conversions are realized during the accretion phase. The matter suppression at high densities prevents any possible impact of the neutrino oscillations on the neutrino heating and hence on the dynamics of the explosion. Furthermore, it changes the interpretation of the Earth matter effect on the SN neutrino signal during the accretion phase, allowing the possibility of the neutrino mass hierarchy discrimination at not too small values of the leptonic mixing angle ${\theta }_{13}$ (i.e., ${sin}^2{\theta }_{13}\gtrsim {10}^{-3}$).

We consider two spatially flat Friedmann-Robertson-Walker spacetimes divided by a timelike thin shell in the nontrivial case in which the inner region of finite extension contains radiation and the outer region is filled with dust. We will then show that, while the evolution is determined by a large set of constraints, an analytical description for the evolution of the bubble radius can be obtained by formally expanding for short times after the shell attains its minimum size. In particular, we will find that a bubble of radiation, starting out with vanishing expansion speed, can be matched with an expanding dust exterior, but not with a collapsing dust exterior, regardless of the dust energy density. The former case can then be used to describe the nucleation of a bubble of radiation inside an expanding dust cloud, although the final configuration contains more energy than the initial dust, and the reverse process, with collapsing radiation transforming into collapsing dust, is therefore energetically favored. We however speculate a (small) decaying vacuum energy or cosmological constant inside dust could still trigger nucleation. Finally, our perturbative (yet analytical) approach can be easily adapted to different combinations of matter inside and outside the shell, as well as to more general surface density, of relevance for cosmology and studies of defect formation during phase transitions.

We consider a cosmological model based upon a noncanonical noncommutative extension of the Heisenberg-Weyl algebra to address the thermodynamical stability and the singularity problem of black holes whose interior are described by the Kantowski-Sachs metric and modeled by a noncommutative extension of the Wheeler-DeWitt equation. We compute the temperature and entropy of these black holes and compare the results with the Hawking values. We observe that it is actually the noncommutativity in the momentum sector that allows for the existence of a minimum in the potential, which is the key to apply the Feynman-Hibbs procedure. It is shown that this noncommutative model generates a nonunitary dynamics that predicts a vanishing probability in the neighborhood of the singularity. This result effectively regularizes the Kantowski-Sachs singularity and generalizes a similar result, previously obtained for the case of Schwarzschild black holes.

In this paper we derive the most general first-order symmetry operator commuting with the Dirac operator in all dimensions and signatures. Such an operator splits into Clifford even and Clifford odd parts which are given in terms of odd Killing-Yano and even closed conformal Killing-Yano inhomogeneous forms, respectively. We study commutators of these symmetry operators and give necessary and sufficient conditions under which they remain of the first-order. In this specific setting we can introduce a Killing-Yano bracket, a bilinear operation acting on odd Killing-Yano and even closed conformal Killing-Yano forms, and demonstrate that it is closely related to the Schouten-Nijenhuis bracket. An important nontrivial example of vanishing Killing-Yano brackets is given by Dirac symmetry operators generated from the principal conformal Killing-Yano tensor [hep-th/0612029]. We show that among these operators one can find a complete subset of mutually commuting operators. These operators underlie separability of the Dirac equation in Kerr-NUT-(A)dS spacetimes in all dimensions [arXiv:0711.0078].

The dynamics of particle, event, and apparent horizons in Friedmann-Lemaitre-Robertson-Walker space are discussed. The apparent horizon is trapping when the Ricci curvature is positive. This simple criterion coincides with the condition for the Kodama-Hayward apparent horizon temperature to be positive and also discriminates between the timelike and spacelike character of the apparent horizon. We discuss also the entropy of apparent cosmological horizons in extended theories of gravity and we use the generalized 2nd law to discard an exact solution of Brans-Dicke gravity as unphysical.

We present a mapping of dynamical graphs and, in particular, the graphs used in the Quantum Graphity models for emergent geometry, to an Ising Hamiltonian on the line graph of a complete graph with a fixed number of vertices. We use this method to study the properties of Quantum Graphity models at low temperature in the limit in which the valence coupling constant of the model is much greater than the coupling constants of the loop terms. Using mean field theory we find that an order parameter for the model is the average valence of the graph. We calculate the equilibrium distribution for the valence as an implicit function of the temperature. In the approximation in which the temperature is low, we find the first two Taylor coefficients of the valence in the temperature expansion. A discussion of the susceptibility function and a generalization of the model are given in the end.

A distinguishable and observable physical property of naked singular regions of the spacetime formed during a gravitational collapse has important implications for both experimental and theoretical relativity. We examine here whether energy can escape physically from naked singular regions to reach either a local or a distant observer within the framework of general relativity. We find that in the case of imploding null dust collapse outgoing singular null geodesics including the Cauchy horizon can be immersed between two Vaidya spacetimes as null boundary layers with nonvanishing positive energy density. Thus energy can be transported from the naked singularity to either a local or a distant observer. An example illustrating that similar considerations can be applied to dust models is given.

We consider generalizations of the entropic accelerating universe recently proposed in [D. A. Easson, P. H. Frampton, and G. F. Smoot, Phys. Lett. B 696, 273 (2011).] and [D. A. Easson, P. H. Frampton, and G. F. Smoot, arXiv:1003.1528.] and show that their background equations can be made equivalent to a model with a dark energy component with a constant parameter of state $w_X=-1+2\gamma /3$, where $\gamma$ is related to the coefficients of the new terms in the Friedmann equations. After discussing all the Friedmann equations for an arbitrary $\gamma$, we show how to recover the standard scalings for dust and radiation. The acoustic scale ${\ell }_A$, related to the peak positions in the pattern of the angular power spectrum of the cosmic microwave background anisotropies, is also computed and yields the stringent bound $|\gamma |\ll 1$. We then argue that future data might be able to distinguish this model from pure $\Lambda \mathrm{CDM}$ (corresponding to $\gamma =0$).

In the full nonlinear cosmological perturbation theory in the leading order of the gradient expansion, all the types of the gauge invariant perturbation variables are defined. The metric junction conditions across the spacelike transition hypersurface are formulated in a manifestly gauge invariant manner. It is manifestly shown that all the physical laws such as the evolution equations, the constraint equations, and the junction conditions can be written using the gauge invariant variables which we defined only. Based on the existence of the universal adiabatic growing mode in the nonlinear perturbation theory and the $\rho$ philosophy where the physical evolution are described using the energy density $\rho$ as the evolution parameter, we give the definitions of the adiabatic perturbation variable and the entropic perturbation variables in the full nonlinear perturbation theory. In order to give the analytic order estimate of the nonlinear parameter $f_{\mathrm{NL}}$, we present the exponent evaluation method. As the models where $f_{\mathrm{NL}}$ changes continuously and becomes large, using the $\rho$ philosophy, we investigate the non-Gaussianity induced by the entropic perturbation of the component which does not govern the cosmic energy density, and we show that in order to obtain the significant non-Gaussianity it is necessary that the scalar field which supports the entropic perturbation is extremely small compared with the scalar field which supports the adiabatic perturbation.

We calculate the vacuum fluctuations that may affect the evolution of cosmological domain walls. Considering domain walls, which are classically stable and have interaction with a scalar field, we show that explicit symmetry violation in the interaction may cause quantum bias that can solve the cosmological domain-wall problem.

We present the first stationary, axisymmetric neutron star models with meridional circulation in general relativity. For that purpose, we developed generally rotating neutron star, a new code based on a fixed-point iteration. We find a two-dimensional set of meridional circulation modes, which differ by the number of vortices in the stream lines of the neutron star fluid. For expected maximal meridional circulation velocities of about $1000\mathrm{km}/\mathrm{s}$, the vortices cause surface deformations of about a percent. The deformations depend on the shape of the vortices close to the surface and increase with the meridional circulation velocity. We also computed models of rotating neutron stars with meridional circulation, where neither the surface rotates nor does the rotation velocity exceed the circulation velocity.

Newly born magnetars are good candidate sources of ultrahigh energy cosmic rays. These objects can in principle easily accelerate particles to the highest energies required to satisfy the ultrahigh energy cosmic ray scenario ($E\sim {10}^{20-21}\mathrm{eV}$), thanks to their important rotational and magnetic energy reservoirs. Their acceleration mechanism, based on unipolar induction, predicts however a hard particle injection that does not fit the observed ultrahigh energy cosmic ray spectrum. Here we show that an adequate distribution of initial voltages among magnetar winds can be found to soften the spectrum. We discuss the effect of these distributions for the stochastic gravitational wave background signature produced by magnetars. The magnetar population characteristics needed to fit the ultrahigh energy cosmic ray spectrum could lead in most optimistic cases to gravitational wave background signals enhanced of up to four orders of magnitudes in the range of frequency 1–100 Hz, compared to the standard predictions. These signals could reach the sensitivities of future detectors such as DECIGO or BBO.

We propose a model for supernovae Ia explosions based on a phase transition to a supersymmetric state which becomes the active trigger for the deflagration starting the explosion in an isolated sub-Chandrasekhar white dwarf star. With two free parameters we fit the rate and several properties of type Ia supernovae and address the gap in the supermassive black hole mass distribution. One parameter is a critical density fit to about $3\times {10}^7\mathrm{g}/\mathrm{cc}$ while the other has the units of a space time volume and is found to be of order 0.05 Gyr $R_E^3$ where $R_E$ is the earth radius. The model involves a phase transition to an exact supersymmetry in a small core of a dense star.

Optical multilayer coatings of high-reflective mirrors significantly determine properties of Fabry-Perot resonators. Thermal (Brownian) noise in these coatings produce excess phase noise which can seriously degrade the sensitivity of high-precision measurements using these cavities. In particular, it is one of the main limiting factors at the current stage in laser gravitational-wave detectors (for example, project LIGO). We present a method to calculate this effect accurately and analyze different strategies to diminish it by optimizing the coating. Traditionally, the effect of the Brownian noise is calculated as if the beam is reflected from the very surface of the mirror’s coating. However, the beam penetrates the coating, and Brownian expansion of the layers leads to dephasing of interference in the coating and consequently to an additional change in the reflected amplitude and phase. Fluctuations in the thickness of a layer change the strain in the medium and hence, due to a photoelastic effect, change the refractive index of this layer. This additional effect should also be considered. It is possible to reduce the noise by changing the total number and thicknesses of high and low refractive layers preserving the reflectivity. We show how an optimized coating may be constructed analytically rather than numerically as before. We also check the possibility of using internal resonant layers, an optimized cap layer, and double mirrors to decrease the thermal noise.

We report results on time-dependent $CP$ asymmetries in $B\to D^{*\mp }{\pi }^{\pm }$ decays based on a data sample containing $657\times {10}^6$ $B\overline{B}$ pairs collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider at the ${\rm Y}(4S)$ resonance. We use a partial reconstruction technique, wherein signal $B\to D^{*\mp }{\pi }^{\pm }$ events are identified using information only from the fast pion from the $B$ decay and the slow pion from the subsequent decay of the $D^{*\mp }$, where the former (latter) corresponds to $D^{*+}(D^{*-})$ final states. We obtain $CP$ violation parameters $S^{+}=+0.061\pm 0.018(\mathrm{stat})\pm 0.012(\mathrm{syst})$ and $S^{-}=+0.031\pm 0.019(\mathrm{stat})\pm 0.015(\mathrm{syst})$.

The renormalization of the third moment of the twist-2 flavor nonsinglet Wilson operator is given to two loops in the ${\mathrm{RI}}^{\prime }/\mathrm{SMOM}$ renormalization scheme. This involves renormalizing the operator itself and the two total derivative operators into which it mixes by inserting it into a quark 2-point function and evaluating the amplitudes at the symmetric subtraction point. The corresponding two loop conversion functions are derived from which the three loop Landau gauge anomalous dimension is deduced. The full set of amplitudes for the two loop Green’s function for each of the operators are given in both the $\overline{\mathrm{MS}}$ and ${\mathrm{RI}}^{\prime }/\mathrm{SMOM}$ schemes.

The branching ratios of the $K^0\to {\pi }^{-}{l}^{+}{\nu }_l\gamma$ ($l=e$, $\mu$) decays, and the $T$-odd triple momenta correlations $\xi =\overrightarrow{q}·[{\overrightarrow{p}}_l\times {\overrightarrow{p}}_{\pi }]/M_K^3$, due to the electromagnetic final state interaction, in these processes are calculated. The contributions on the order of ${\omega }^{-1}$ and ${\omega }^0$ to the corresponding amplitudes are treated exactly. For the branching ratios and $T$-odd correlation in $K^0\to {\pi }^{-}{e}^{+}{\nu }_e\gamma$ decay, the corrections on the order of $\omega$ are estimated and demonstrated to be small. The results for the branching ratios are in good agreement with the previous ones. The $T$-odd triple momenta correlations in $K_{l3\gamma }^0$ decays are calculated for the first time. The values of the $\xi$-odd asymmetry are on the order of ${10}^{-3}$ and ${10}^{-2}$ in the $K^0\to {\pi }^{-}{\mu }^{+}{\nu }_{\mu }\gamma$ and $K^0\to {\pi }^{-}{e}^{+}{\nu }_e\gamma$ decays, respectively.

Many theoretical and experimental results on the reach of the Large Hadron Collider are based on the minimal supergravity (mSUGRA)-inspired scenario with universal soft supersymmetry-breaking parameters at the apparent gauge coupling unification scale. We study signals for supersymmetric models in which the sparticle mass range is compressed compared to mSUGRA, using cuts like those employed by ATLAS for 2010 data. The acceptance and the cross-section times acceptance are found for several model lines that employ a compression parameter to smoothly interpolate between the mSUGRA case and the extreme case of degenerate gaugino masses at the weak scale. For models with moderate compression, the reach is not much worse, and can even be substantially better, than the mSUGRA case. For very compressed mass spectra, the acceptances are drastically reduced, especially when a more stringent effective mass cut is chosen.