The properties of the two-flavored Gross-Neveu model in the ($1+1$)-dimensional $R^1\times S^1$ spacetime with compactified space coordinate are investigated in the presence of the isospin chemical potential ${\mu }_I$. The consideration is performed in the limit $N_c\to \infty$, i.e. in the case with infinite number of colored quarks. It is shown that at $L=\infty$ ($L$ is the length of the circumference $S^1$) the pion condensation phase is realized for arbitrary small nonzero ${\mu }_I$. At finite values of $L$, the phase portraits of the model in terms of parameters $\nu \sim {\mu }_I$ and $\lambda \sim 1/L$ are obtained both for periodic and antiperiodic boundary conditions of the quark field. It turns out that in the plane $(\lambda ,\nu )$ there is a strip $0\le \lambda <{\lambda }_c$ which lies as a whole inside the pion condensed phase. In this phase the pion condensation gap is an oscillating function vs both $\lambda$ (at fixed $\nu$) and $\nu$ (at fixed $\lambda$).

Using the cut-and-paste procedure, we construct static and dynamic, plane symmetric wormholes by surgically grafting together two spacetimes of plane symmetric vacuum solutions with a negative cosmological constant. These plane symmetric wormholes can be interpreted as domain walls connecting different universes, having planar topology, and upon compactification of one or two coordinates, cylindrical topology or toroidal topology, respectively. A stability analysis is carried out for the dynamic case by taking into account specific equations of state, and a linearized stability analysis around static solutions is also explored. It is found that thin-shell wormholes made of a dark energy fluid or of a cosmological constant fluid are stable, while thin-shell wormholes made of phantom energy are unstable.

A class of exact solutions to Einstein’s equations is presented, which describes accelerating photon rockets in the de Sitter and anti-de Sitter universes. These are particular members of the Robinson-Trautman family of axially symmetric spacetimes with pure radiation. In particular, generalizations of (type D) Kinnersley’s rockets and (type II) Bonnor’s rockets to the case of a nonvanishing cosmological constant are given. Some of the main physical properties of these solutions are investigated, and their relation to the C-metric solution which describes uniformly accelerated black holes is also given.

Gravitational radiation in plane-symmetric space-times can be encoded in a complex potential, satisfying a nonlinear wave equation. An effective energy tensor for the radiation is given, taking a scalar-field form in terms of the potential, entering the field equations in the same way as the matter energy tensor. It reduces to the Isaacson energy tensor in the linearized, high-frequency approximation. An energy conservation equation is derived for a quasilocal energy, essentially the Hawking energy. A transverse pressure exerted by interacting low-frequency gravitational radiation is predicted.

We adopt the covariant anomaly cancellation method as well as the effective action approach to obtain the Hawking radiation from the Reissner-Nordström blackhole with a global monopole falling in the class of the most general spherically symmetric charged blackhole ($\sqrt{-g}\ne 1$), using only covariant boundary conditions at the event horizon.

We develop the Hadamard renormalization of the stress-energy tensor for a massive scalar field theory defined on a general spacetime of arbitrary dimension. Our formalism could be helpful in treating some aspects of the quantum physics of extra spatial dimensions. More precisely, for spacetime dimensions up to six, we explicitly describe the Hadamard renormalization procedure and for spacetime dimensions from 7 to 11, we provide the framework permitting the interested reader to perform this procedure explicitly in a given spacetime. We complete our study (i) by considering the ambiguities of the Hadamard renormalization of the stress-energy tensor and the corresponding ambiguities for the trace anomaly, (ii) by providing the expressions of the gravitational counterterms involved in the renormalization process, and (iii) by discussing the connections between Hadamard renormalization and renormalization in the effective action. All our results are expanded on standard bases for Riemann polynomials constructed from group theoretical considerations and thus given on irreducible forms.

The primordial spectra are calculated using dispersion relations that deviate from the relativistic one above a certain energy scale $\Lambda$. We determine the properties of the leading modifications with respect to the standard spectra when $\Lambda \gg H$, where $H$ is the Hubble scale during inflation. To be generic, we parameterize the lowest order deviation from the relativistic law by $\alpha$, the power of $P/\Lambda$, where $P$ is the proper momentum. When working in the asymptotic vacuum, the leading modification scales as $(H/\Lambda {)}^{\alpha }$ for all $\alpha$, except for a discrete set where the power is higher. Moreover, this modification is robust against introducing higher order terms in the dispersion relation. We then algebraically deduce the modifications of scalar and tensor power spectra in slow-roll inflation from modifications calculated in de Sitter space. The modifications do not exhibit oscillations unless the dispersion relation induces some nonadiabaticity near a given scale. Finally, we explore the much less studied regime where $H$ and $\Lambda$ are comparable. Our results indicate that the project of reconstructing the inflaton potential cannot be pursued without making some hypothesis about the dispersion relation of the fluctuation modes.

We study the evolution of biased domain walls in the early universe. We explicitly discuss the roles played by the surface tension and volume pressure in the evolution of the walls, and quantify their effects by looking at the collapse of spherical wall solutions. We then apply our results to a particular mechanism, known as the devaluation scenario, in which the dynamics of biased domain walls was suggested as a possible solution to the cosmological constant problem. Our results indicate that devaluation will, in general, lead to values of the cosmological constant that differ by several orders of magnitude from the observationally inferred value, ${\rho }_{\mathrm{vac}}^{1/4}\sim {10}^{-3}\mathrm{eV}$. We also argue that the reasons behind this are not specific to a particular realization, and are expected to persist in any scenario of this kind, except if a low-energy cutoff on the spectra of vacuum energy densities, of the order of the critical density at the present time, is postulated. This implies that any such scenario will require a fine-tuning similar to the usual one.

We investigate the correlation of gravitational lensing of the cosmic microwave background (CMB) with several tracers of large-scale structure, including luminous red galaxies (LRGs), quasars, and radio sources. The lensing field is reconstructed based on the CMB maps from the Wilkinson Microwave Anisotropy Probe (WMAP) satellite; the LRGs and quasars are observed by the Sloan Digital Sky Survey (SDSS); and the radio sources are observed in the NRAO VLA Sky Survey (NVSS). Combining all three large-scale structure samples, we find evidence for a positive cross correlation at the $2.5\sigma$ level ($1.8\sigma$ for the SDSS samples and $2.1\sigma$ for NVSS); the cross correlation amplitude is $1.06\pm 0.42$ times that expected for the WMAP cosmological parameters. Our analysis extends other recent analyses in that we carefully determine bias-weighted redshift distribution of the sources, which is needed for a meaningful cosmological interpretation of the detected signal. We investigate contamination of the signal by galactic emission, extragalactic radio and infrared sources, thermal and kinetic Sunyaev-Zel’dovich effects, and the Rees-Sciama effect, and find all of them to be negligible.

We cross correlate large-scale structure (LSS) observations from a number of surveys with cosmic microwave background (CMB) anisotropies from the Wilkinson Microwave Anisotropy Probe (WMAP) to investigate the integrated Sachs-Wolfe (ISW) effect as a function of redshift, covering $z\sim 0.1–2.5$. Our main goal is to go beyond reporting detections towards developing a reliable likelihood analysis that allows one to determine cosmological constraints from ISW observations. With this in mind we spend a considerable amount of effort in determining the redshift-dependent bias and redshift distribution ($b(z)\times dN/dz$) of these samples by matching with spectroscopic observations where available, and analyzing autopower spectra and cross-power spectra between the samples. Because of wide redshift distributions of some of the data sets we do not assume a constant-bias model, in contrast to previous work on this subject. We only use the LSS data sets for which we can extract such information reliably and as a result the data sets we use are 2-Micron All Sky Survey (2MASS) samples, Sloan Digital Sky Survey (SDSS) photometric Luminous Red Galaxies, SDSS photometric quasars, and NRAO VLA Sky Survey (NVSS) radio sources. We make a joint analysis of all samples constructing a full covariance matrix, which we subsequently use for cosmological parameter fitting. We report a $3.7\sigma$ detection of ISW combining all the data sets. We do not find significant evidence for an ISW signal at $z>1$, in agreement with theoretical expectation in the $\Lambda \mathrm{CDM}$ model. We combine the ISW likelihood function with weak lensing of CMB (hereafter Paper II [C. M. Hirata, S. Ho, N. Padmanabhan, U. Seljak, and N. A. Bahcall, arXiv:0801.0644.]) and CMB power spectrum to constrain the equation of state of dark energy and the curvature of the Universe. While ISW does not significantly improve the constraints in the simplest six-parameter flat $\Lambda \mathrm{CDM}$ model, it improves constraints on seven-parameter models with curvature by a factor of 3.2 (relative to WMAP alone) to ${\Omega }_K=-{0.004}_{-0.020}^{+0.014}$, and with dark energy equation of state by 15% to $w=-{1.01}_{-0.40}^{+0.30}$ [posterior median with “$1\sigma$” (16th–84th percentile) range]. A software package for calculating the ISW likelihood function can be downloaded at http://www.astro.princeton.edu/~shirley/ISW_WL.html.

We report on lattice simulations of 16 supercharge $SU(N)$ Yang-Mills quantum mechanics in the ’t Hooft limit. Maldacena duality conjectures that in this limit the theory is dual to IIA string theory, and, in particular, that the behavior of the thermal theory at low temperature is equivalent to that of certain black holes in IIA supergravity. Our simulations probe the low temperature regime for $N\le 5$ and the intermediate and high temperature regimes for $N\le 12$. We observe ’t Hooft scaling, and at low temperatures our results are consistent with the dual black hole prediction. The intermediate temperature range is dual to the Horowitz-Polchinski correspondence region, and our results are consistent with continuous behavior there. We include the Pfaffian phase arising from the fermions in our calculations where appropriate.

A new class of twistor string theories was recently constructed by Abou-Zeid, Hull, and Mason. The most interesting one of these theories has the particle content of $\mathcal{N}=8$ supergravity. Arguments are given for the vanishing of the ($+--$)-helicity amplitude for gravitons which suggest that this theory describes a chiral $\mathcal{N}=8$ supergravity rather than Einstein supergravity.

Cross sections of the $e^{+}{e}^{-}$ annihilate into one photon and two vector mesons, such as $J/\psi \rho$, $J/\psi \varphi$, and $\rho \varphi$ at the center of mass energy $\sqrt{s}=10.58\mathrm{GeV}$ are calculated. These shed light on the measurement of the $e^{+}{e}^{-}$ annihilation cross section via radiative return in $B$ factories. At another center of mass energy $\sqrt{s}=3.097\mathrm{GeV}$, namely, the $J/\psi$ resonance peak, the cross sections for the processes $e^{+}{e}^{-}\to \gamma VV$ and $e^{+}{e}^{-}\to \gamma \gamma V$ (with $V$ being $\rho$, $\omega$, or $\varphi$) are calculated with similar methods. These calculations give an estimation of the background levels in the study of radiative or double radiative decays of $J/\psi$.

We study flavor-changing neutral current and $CP$ violations in the minimal supersymmetric left-right model. We calculate the beyond-standard-model contributions to the neutral kaon mixing $\Delta M_K$ and $ϵ$, and find it is possible to have a numerical cancellation between the contributions from the right-handed gauge boson and supersymmetric box diagram. With the cancellation, the right-handed $W$-boson mass scale can be lowered to about 2 TeV, well within the search limit of LHC.

We provide the analysis of charmless two-body $B\to VP$ decays under the framework of the soft collinear effective theory (SCET), where $V(P)$ denotes a light vector (pseudoscalar) meson. Besides the leading power contributions, some power corrections (chiraly enhanced penguins) are also taken into account. Using the current available $B\to PP$ and $B\to VP$ experimental data on branching fractions and $CP$ asymmetry variables, we find two kinds of solutions in ${\chi }^2$ fit for the 16 nonperturbative inputs which are essential in the 87 $B\to PP$ and $B\to VP$ decay channels. Chiraly enhanced penguins can change several charming penguins sizably, since they share the same topology. However, most of the other nonperturbative inputs and predictions on branching ratios and $CP$ asymmetries are not changed too much. With the two sets of inputs, we predict the branching fractions and $CP$ asymmetries of other modes especially $B_s\to VP$ decays. The agreements and differences with results in QCD factorization and perturbative QCD approach are analyzed. We also study the time-dependent $CP$ asymmetries in channels with $CP$ eigenstates in the final states and some other channels such as ${\overline{B}}^0/B^0\to {\pi }^{\pm }{\rho }^{\mp }$ and ${\overline{B}}_s^0/B_s^0\to K^{\pm }{K}^{*\mp }$. In the perturbative QCD approach, the $(S-P)(S+P)$ penguins in annihilation diagrams play an important role. Although they have the same topology with charming penguins in SCET, there are many differences between the two objects in weak phases, magnitudes, strong phases, and factorization properties.

We study the particle multiplicity in a jet or subjet as derived from an energy-multiplicity 2-particle correlation. This definition avoids the notion of a globally fixed jet axis and allows for the study of smaller jet cone openings in a more stable way. The results are sensitive to the mean color current $⟨C{⟩}_{A_0}$ in the jet from primary parton $A_0$, which takes into account intermediate partonic processes in the subjet production where $C_F<⟨C{⟩}_{A_0}<N_c$ at high energies. We generalize previous calculations in the leading logarithmic approximation (LLA). The size of the effects related to this jet axis definition is computed for multiplicities in subjets with different opening angles and energies by including contributions from the modified LLA and next-to-modified LLA to the leading order QCD results.

We calculate the leading order diphoton generalized distribution amplitudes by calculating the amplitude of the process ${\gamma }^{*}\gamma \to \gamma \gamma$ in the low energy and high photon virtuality region at the Born order and in the leading logarithmic approximation. As in the case of the anomalous photon structure functions, the $\gamma \gamma$ generalized distribution amplitudes exhibit a characteristic $\ln Q^2$ behavior and obey inhomogeneous QCD evolution equations.

In the framework of the seesaw models with triplets of fermions, we evaluate the decay rates of $\mu \to e\gamma$ and $\tau \to l\gamma$ transitions. We show that although, due to neutrino mass constraints, those rates are in general expected to be well under the present experimental limits, this is not necessarily always the case. Interestingly enough, the observation of one of those decays in planned experiments would nevertheless contradict bounds stemming from present experimental limits on the $\mu \to eee$ and $\tau \to 3l$ decay rates, as well as from $\mu$ to $e$ conversion in atomic nuclei. Such detection of radiative decays would therefore imply that there exist sources of lepton flavor violation not associated to triplet fermions.

We consider the “second-class current” decay ${\tau }^{-}\to {\pi }^{-}\eta {\nu }_{\tau }$ from several points of view. We first focus on the decay rate as expected within standard weak interaction and QCD due to isospin violation. The decay contributions divide into $P$- and $S$-wave parts. The former can be reliably estimated using the $\rho \eta \pi$ coupling inferred from the rates and Dalitz-plot distributions of $\eta \to 3\pi$ decays. The somewhat larger $S$-wave part, which was previously computed using chiral perturbation theory, is estimated from a simple $\overline{q}q$ model. Both estimates of the $S$-wave part depend on whether the $a_0(980)$ scalar particle is a $\overline{q}q$ or some other (4-quark) state. Finally, we discuss genuinely new, non-$V-A$ scalar weak interactions. The ${\tau }^{-}\to {\pi }^{-}\eta {\nu }_{\tau }$ decay provides information on this question, which nicely complements that from precision $\beta$ decay experiments. In summary, we discuss the possible implications of putative values of the branching fraction $\mathcal{B}({\tau }^{-}\to {\pi }^{-}\eta {\nu }_{\tau })$. In the case of larger values, in particular, of the $S$-wave part, not only will detection of the decay be more likely and more reliable, its implications will be more far-reaching and interesting.

We study the transformation of multipolar decompositions of gravitational radiation under rotations and boosts. Rotations to the remnant black hole’s frame simplify the waveforms from the merger of generic spinning black hole binaries. Boosts may be important to get an accurate gravitational-wave phasing, especially for configurations leading to large recoil velocities of the remnant. As a test of the formalism we revisit the classic problem of point particles falling into a Schwarzschild black hole. Then we highlight by specific examples the importance of choosing the right frame in numerical simulations of unequal mass, spinning binary black-hole mergers.