In the semi-light-cone gauge $g_{\mathrm{ab}}{=e}^{2\phi }{\delta }_{\mathrm{ab}},$ ${\overline{\gamma }}^{+}\theta =0,$ we evaluate the φ-dependent effective action for the pp-wave Green-Schwarz (GS) superstring in both harmonic and group coordinates. When we compute the fermionic φ-dependent effective action in harmonic coordinates, we find a new triangular one-loop Feynman diagram. We show that the bosonic φ-dependent effective action cancels with the fermionic one, indicating that the pp-wave GS superstring is a conformal field theory. We introduce the group coordinates preserving $\mathrm{SO}\left(4\right)\mathrm{}\times \mathrm{SO}\left(4\right)\mathrm{}$ and conformal symmetry. Group coordinates are interesting because vertex operators take simple forms in them. The new feature of the group coordinates is that there are logarithmic divergences from n-gons, so that the divergent structure is more complicated than in harmonic coordinates. After summing over all contributions from n-gons, we show that in group coordinates the GS superstring on a pp-wave RR background is still a conformal field theory.

We consider a spaceborne gravitational wave (GW) detector formed by three spacecraft in a linear array, coherently exchanging laser beams and using the data combinations of time-delay interferometry (TDI). We previously showed how the measured time series of Doppler shifts in the six one-way laser links between spacecraft pairs in a general unequal-arm triangular configuration can be combined, using TDI, to exactly cancel the otherwise overwhelming phase noise of the lasers while retaining sensitivity to GWs. Here we apply TDI, unfolding the general triangular configuration, to the special case of a linear array of three spacecraft. We show that such an array (“SyZyGy”) has, compared with an equilateral triangle GW detector of the same scale, a degraded (but non-zero) sensitivity at low frequencies $[f\ll c/(\mathrm{array}\mathrm{}\mathrm{size}\left)\right]$ but similar peak and high-frequency sensitivities to GWs. We develop the GW and noise responses, noting that in this geometrical case only one TDI combination is GW sensitive showing a relatively simple 6-pulse response to an incident GW burst. Sensitivity curves are presented for SyZyGys having various arm lengths. A number of technical simplifications result from the linear configuration. These include only one faceted (e.g. cubical) proof mass per spacecraft, intraspacecraft laser metrology needed only at the central spacecraft, placement in an appropriate orbit can reduce Doppler drifts so that no laser beam modulation is required for ultrastable oscillator noise calibration, and little or no time-dependent articulation of the telescopes to maintain pointing. Because SyZyGy’s sensitivity falls off more sharply at low frequency than that of an equilateral triangular array, it may be most useful for GW observations in the band between those of ground-based interferometers $(\sim 10–2000\mathrm{Hz})$ and the Laser Interferometer Space Antenna $(\sim {10}^{-4}–{10}^{-1}\mathrm{Hz}).\mathrm{}$ SyZyGy with $\sim 1$ light-second scale could, for the same instrumental assumptions as LISA, make observations in this intermediate frequency GW band with $5\sigma$ sensitivity to sinusoidal waves $\simeq 2.5\times {10}^{-23}$ in a year’s integration.

We study the “Casimir” energy of a minimally coupled, real, massless scalar field outside a spherically symmetric background potential. We obtain a general expression for the null energy condition in d dimensions and explicit expressions for a perfectly reflecting spherical boundary in $3+1$ and $2+1$ dimensions. In these cases, the null energy condition is always violated for radial motion and obeyed for azimuthal motion. Nevertheless, the averaged null energy condition is always obeyed.

It is proposed that the cooling of a thermalized $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ gauge theory can be formulated in terms of a cascade involving three effective theories with successively reduced (and spontaneously broken) gauge symmetries, $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}\to \mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}^{N-1}\to {\mathrm{Z}}_N.$ The approach is based on the assumption that away from a phase transition the bulk of the quantum interaction inherent to the system is implicitly encoded in the (incomplete) classical dynamics of a collective part made of low-energy condensed degrees of freedom. The properties of (some of the) statistically fluctuating fields are determined by these condensate(s). This leads to a quasiparticle description at the tree level. It appears that radiative corrections, which are sizable at large gauge coupling, do not change the tree-level picture qualitatively. The thermodynamic self-consistency of the quasi-particle approach implies nonperturbative evolution equations for the associated masses. The temperature dependence of these masses, in turn, determines the evolution of the gauge coupling(s). The hot gauge system approaches the behavior of an ideal gas of massless gluons at asymptotically large temperature. A negative equation of state is possible at a stage where the system is about to settle into the phase of the (spontaneously broken) ${\mathrm{Z}}_N$ symmetry.

Using the path integral method (Fujikawa’s method) we calculate anomalies in noncommutative gauge theories with fermions in the bifundamental and adjoint representations. We find that axial and chiral gauge anomalies coming from nonplanar contributions emerge in the low noncommutative momentum limit $p^{\mu }\left(\equiv {\theta }^{\mu \nu }{p}_{\nu }\right)\to 0.$ The adjoint chiral fermion carries no anomaly in the nonplanar sector in $D=4k(k=1,2,\dots ,)$ dimensions. It is naturally shown using the path integral method that anomalies in the nonplanar sector originate in UV/IR mixing.

We study the motion of particles and light in a space-time of a five-dimensional rotating black hole. We demonstrate that the Myers-Perry metric describing such a black hole, in addition to three Killing vectors, also possesses a Killing tensor. As a result, the Hamilton-Jacobi equations of motion allow a separation of variables. Using first integrals we present the equations of motion in the first-order form. We describe different types of motion of particles and light and study some interesting special cases. We prove that there are no stable circular orbits in equatorial planes in the background of this metric.

We present a systematic treatment of the initial conditions and evolution of cosmological perturbations in a universe containing photons, baryons, neutrinos, cold dark matter, and a scalar quintessence field. By formulating the evolution in terms of a differential equation involving a matrix acting on a vector comprised of the perturbation variables, we can use the familiar language of eigenvalues and eigenvectors. As the largest eigenvalue of the evolution matrix is fourfold degenerate, it follows that there are four dominant modes with a nondiverging gravitational potential at early times, corresponding to adiabatic, cold dark matter isocurvature, baryon isocurvature and neutrino isocurvature perturbations. We conclude that quintessence does not lead to an additional independent mode.

General $O\left(\alpha \right)$ radiative corrections to lattice actions may be interpreted as counterterms that give additive contributions to the one loop renormalization of the anisotropy. The effect of changing the radiative coefficients is thus easily calculable. In particular, the results obtained in a previous paper for Landau mean link improved actions apply in any tadpole improvement scheme. We explain how this method can be exploited when tuning radiatively improved actions. Efficient methods for self-consistently tuning tadpole improvement factors are also discussed.

Elitzur’s theorem stating the impossibility of spontaneous breaking of local symmetries in a gauge theory is reexamined. The existing proofs of this theorem rely on gauge invariance as well as positivity of the weight in the Euclidean partition function. We examine the validity of Elitzur’s theorem in gauge theories for which the Euclidean measure of the partition function is not positive definite. We find that Elitzur’s theorem does not follow from gauge invariance alone. We formulate a general criterion under which spontaneous breaking of local symmetries in a gauge theory is excluded. Finally we illustrate the results in an exactly solvable two dimensional Abelian gauge theory.

We study the role of the strange quark mass in color-flavor locked matter. An effective interaction between kaons and particle-hole excitations near the Fermi surface is important and should be included in the effective Lagrangian. The new picture is based on the reasonable assumption of quark-hadron continuity. For a nonzero strange-quark mass, there is the possibility that both antikaon and kaon condensates may occur at different densities. A novel phase diagram of high-density QCD is given, which is different from that given in previous literature. The implications of the configuration are discussed briefly.

It has recently been proposed that all fundamental fermion masses (whether Dirac or Majorana) come from effective dimension-five operators in the context of a truly minimal left-right model. We show how a particularly economical scheme emerges in a supersymmetric framework, where chiral symmetry breaking originates in the gaugino sector.

We propose a new reduction mechanism which allows one to construct n-particle (super)conformal theories with a pairwise interaction starting from a composite system involving $n\left(n-1\right)/2+1$ copies of the ordinary (super)conformal mechanics. Applications of the scheme include an $N=4\mathrm{}$ superconformal extension for a complexification of the Calogero model and a $D(2,1\mathrm{}|\alpha )$-invariant n-particle system.

In this paper we evaluate strong decay amplitudes and partial widths of strange mesons (strangeonia and kaonia) in the ${}^3{P}_0$ decay model. We give numerical results for all energetically allowed open-flavor two-body decay modes of all $n\overline{s}$ and $s\overline{s}$ strange mesons in the $1S,$ $2S,$ $3S,$ $1P,$ $2P,$ $1D$ and $1F$ multiplets, comprising strong decays of a total of 43 resonances into 525 two-body modes, with 891 numerically evaluated amplitudes. This set of resonances includes all strange $q\overline{q}$ states with allowed strong decays expected in the quark model up to ca. 2.2 GeV. We use standard nonrelativistic simple harmonic oscillator quark model wave functions to evaluate these amplitudes, and quote numerical results for all amplitudes present in each decay mode. We also discuss the status of the associated experimental candidates, and note which states and decay modes would be especially interesting for future experimental study at hadronic, $e^{+}{e}^{-}$ and photoproduction facilities. These results should also be useful in distinguishing conventional quark model mesons from exotica such as glueballs and hybrids through their strong decays.

We present final measurements of 13 charmless hadronic B decay modes from the CLEO experiment. The decay modes include the ten $\pi \pi ,$ $K\pi ,$ and KK final states and new limits on dibaryonic final states, $p\overline{p},$ $p\overline{\Lambda },$ and $\Lambda \overline{\Lambda },$ as well as a new determination of the ratio $\mathcal{B}\left(\overrightarrow{B}DK\right)/\mathcal{B}\left(\overrightarrow{B}D\pi \right).\mathrm{}$ The results are based on the full CLEO II and CLEO III data samples totalling $15.3{\mathrm{fb}}^{-1}$ at the ${\rm Y}\mathrm{}\left(4S\right),$ and supercede previously published results.

The infinite matrices in Witten’s vertex are easy to diagonalize. It just requires some $SL(2,R)$ lore plus a Watson-Sommerfeld transformation. We calculate the eigenvalues of all Neumann matrices for all scale dimensions s, both for matter and ghosts, including fractional s which we use to regulate the difficult $s=0\mathrm{}$ limit. We find that $s=1\mathrm{}$ eigenfunctions just acquire a p term, and x gets replaced by the midpoint position.

We discuss the definition of particle velocity in doubly special relativity theories. The general formula relating the velocity and four-momentum of the particle is given.

In this paper, the dynamical equations and junction conditions at the interface between adjacent layers of different elastic properties for an elastic deformable astronomical body in the first post-Newtonian approximation of Einstein theory of gravity are discussed in both rotating Cartesian coordinates and rotating spherical coordinates. The unperturbed rotating body (the ground state) is described as a uniformly rotating, stationary and axisymmetric configuration in an asymptotically flat space-time manifold. Deviations from the equilibrium configuration are described by means of a displacement field. In terms of the formalism of relativistic celestial mechanics developed by Damour, Soffel, and Xu, and the framework established by Carter and Quintana the post-Newtonian equations of the displacement field and the symmetric trace-free shear tensor are obtained. Corresponding post-Newtonian junction conditions at interfaces, also the outer surface boundary conditions are presented, which is the extension of Wahr’s Newtonian junction conditions without rotating.

We use the procedure of pinched-weight finite energy sum rules to determine the operator product expansion (OPE) coefficients $a_6,\dots {,a}_{16}$ of the flavor ud $V-A$ correlator in terms of existing hadronic $\tau$ decay data. We show by appropriate weight choices that the error on the dominant $d=6\mathrm{}$ contribution, which is known to be related to the $\overrightarrow{K}\pi \pi$ matrix elements of the electroweak penguin operator in the chiral limit, may be reduced to below the $\sim 15\%$ level. The values we obtain for OPE coefficients with $d>\mathrm{}8\mathrm{}$ are shown to naturally account for the discrepancies between our results for the $d=6\mathrm{}$ and $d=8\mathrm{}$ terms and those of previous analyses, which were obtained neglecting $d>\mathrm{}8\mathrm{}$ contributions.

A slow $J/\psi$ excess exists in the inclusive $\overrightarrow{B}J/\psi +X$ spectrum, and is indicative of some hadronic effect. From the color octet nature of the $c\overline{c}$ pair in $\overrightarrow{b}c\overline{c}s$ decay, one such possibility would be $\overrightarrow{B}J/\psi {+K}_g$ decay, where $K_g$ is a hybrid resonance with $\overline{s}\mathrm{gq}$ constituents. We show that a $K_g$ resonance of $\sim 2\mathrm{GeV}$ mass and suitably broad width could be behind the excess.