We present a simple set of rules for obtaining the imaginary part of a self-energy diagram at finite temperature as a product of tree amplitudes. These diagrams correspond to physical scattering amplitudes.

Massive theories of Abelian p forms are quantized in a generalized path representation that leads to a description of the phase space in terms of a pair of dual nonlocal operators analogous to the Wilson loop and the ’t Hooft disorder operators. Special attention is devoted to the study of the duality between the topologically massive and self-dual models in $2+1$ dimensions. It is shown that these models share a geometric representation in which just one nonlocal operator suffices to describe the observables.

It has recently been suggested that, in the large N limit, a particular four dimensional gauge theory is indistinguishable from six dimensional conformal field theory with (0,2) supersymmetry compactified on a torus. We give further evidence for this correspondence by studying the Seiberg-Witten curve for the “deconstructed” theory and demonstrating that along the reduced Coulomb branch of moduli space (at the intersection of the Higgs and Coulomb branches) it describes the low energy physics on a stack of M5-branes on a torus, which is the (0,2) theory on a torus as claimed. The M-theory construction helps to clarify the enhancement of supersymmetry in the deconstructed theory at low energies, and demonstrates its stability to radiative and instanton corrections. We demonstrate the role of the theta vacuum in the deconstructed theory. We point out that, by varying the theta parameters and gauge couplings in the deconstructed theory, the complex structure of the torus can be chosen arbitrarily, and the torus is not metrically ${\mathrm{S}}^1\times {\mathrm{S}}^1$ in general.

We derive a renormalization group formalism for the Randall-Sundrum scenario, where the renormalization scale is set by a floating compactification radius. While inspired by the AdS-CFT conjecture, our results are derived concretely within higher-dimensional effective field theory. Matching theories with different radii leads to running hidden brane couplings. The hidden brane Lagrangian consists of four-dimensional local operators constructed from the induced value of the bulk fields on the brane. We find hidden Lagrangians which are nontrivial fixed points of the RG flow. Calculations in RS1 can be greatly simplified by “running down” the effective theory to a small radius. We demonstrate these simplifications by studying the Goldberger-Wise stabilization mechanism. In this paper, we focus on the classical and tree-level quantum field theory of bulk scalar fields, which demonstrates the essential features of the RG in the simplest context.

We classify all spherically symmetric and homothetic spacetimes that are allowed kinematically by constructing them from a small number of building blocks. We then restrict attention to a particular dynamics, namely perfect fluid matter with the scale-free barotropic equation of state $p=\alpha \mu$ where $0<~\alpha <1\mathrm{}$ is a constant. We assign conformal diagrams to all solutions in the complete classification of Carr and Coley, and so establish which of the kinematic possibilities are realized for these dynamics. We pay particular attention to those solutions which arise as critical solutions during gravitational collapse.

This paper describes an approach that uses flat-spacetime estimators to estimate the manifold dimension of causal sets that can be faithfully embedded into curved spacetimes. The approach is invariant under coarse-graining and can be implemented independently of any specific curved spacetime. Results are given based on causal sets generated by random sprinklings into conformally flat spacetimes in 2, 3, and 4 dimensions, as well as one generated by a percolation dynamics.

We report a new implementation for axisymmetric simulation in full general relativity. In this implementation, the Einstein equations are solved using the Nakamura-Shibata formulation with the so-called cartoon method to impose an axisymmetric boundary condition, and the general relativistic hydrodynamic equations are solved using a high-resolution shock-capturing scheme based on an approximate Riemann solver. As tests, we performed the following simulations: (i) long-term evolution of nonrotating and rapidly rotating neutron stars, (ii) long-term evolution of neutron stars of a high-amplitude damping oscillation accompanied with shock formation, (iii) collapse of unstable neutron stars to black holes, and (iv) stellar collapses to neutron stars. Tests (i)–(iii) were carried out with the $\Gamma$-law equation of state, and test (iv) with a more realistic parametric equation of state for high-density matter. We found that this new implementation works very well: It is possible to perform the simulations for stable neutron stars for more than 10 dynamical time scales, to capture strong shocks formed at stellar core collapses, and to accurately compute the mass of black holes formed after the collapse and subsequent accretion. In conclusion, this implementation is robust enough to apply to astrophysical problems such as stellar core collapse of massive stars to a neutron star, and black hole, phase transition of a neutron star to a high-density star, and accretion-induced collapse of a neutron star to a black hole. The result for the first simulation of stellar core collapse to a neutron star started from a realistic initial condition is also presented.

We explore the dynamics of the r-modes in accreting neutron stars in two ways. First, we explore how dissipation in the magnetoviscous boundary layer (MVBL) at the crust-core interface governs the damping of r-mode perturbations in the fluid interior. Two models are considered: one assuming an ordinary-fluid interior, the other taking the core to consist of superfluid neutrons, type II superconducting protons, and normal electrons. We show, within our approximations, that no solution to the magnetohydrodynamic equations exists in the superfluid model when both the neutron and proton vortices are pinned. However, if just one species of vortex is pinned, we can find solutions. When the neutron vortices are pinned and the proton vortices are unpinned there is much more dissipation than in the ordinary-fluid model, unless the pinning is weak. When the proton vortices are pinned and the neutron vortices are unpinned the dissipation is comparable or slightly less than that for the ordinary-fluid model, even when the pinning is strong. We also find in the superfluid model that relatively weak radial magnetic fields $\sim {10}^9\mathrm{G}{(10\mathrm{}}^8\mathrm{K}{/T)}^2$ greatly affect the MVBL, though the effects of mutual friction tend to counteract the magnetic effects. Second, we evolve our two models in time, accounting for accretion, and explore how the magnetic field strength, the r-mode saturation amplitude, and the accretion rate affect the cyclic evolution of these stars. If the r-modes control the spin cycles of accreting neutron stars we find that magnetic fields can affect the clustering of the spin frequencies of low mass x-ray binaries and the fraction of these that are currently emitting gravitational waves.

We present the Noether-charge realization of the diffeomorphism invariance of the gravitational theory in the covariant phase space formalism. With the help of the null tetrad well defined on the horizon, it is shown that the central term vanishes for the reduced diffeomorphism algebra on the Killing horizon with respect to a large class of vector fields in the vacuum general relativity.

We study the dynamics of a scalar field in brane cosmology. We assume that the scalar field is confined in our four-dimensional world. As for the potential of the scalar field, we discuss three typical models: (1) a power-law potential, (2) an inverse-power-law potential, and (3) an exponential potential. We show that the behavior of the scalar field is very different from that in conventional cosmology when the energy density square of the term dominates.

A combination of recent observational results has given rise to what is currently known as the dark energy problem. Although several possible candidates have been extensively discussed in the literature, the nature of this dark energy component is not well understood at present. In this paper we investigate some cosmological implications of another dark energy candidate: an exotic fluid known as the Chaplygin gas, which is characterized by an equation of state $p=-A/\rho ,$ where A is a positive constant. By assuming a flat scenario driven by nonrelativistic matter plus a Chaplygin gas dark energy we study the influence of such a component on the statistical properties of gravitational lenses. A comparison between the predicted age of the universe and the latest age estimates of globular clusters is also included and the results briefly discussed. In general, we find that the behavior of this class of models may be interpreted as an intermediary case between the standard model and the cold dark matter model with a cosmological constant scenarios.

We investigate resonant spin-flavor (RSF) conversions of supernova neutrinos which are induced by the interaction of neutrino magnetic moment and supernova magnetic fields. From the formulation which includes all three-flavor neutrinos and antineutrinos, we give a new crossing diagram that includes not only ordinary Mikheyev-Smirnov-Wolfenstein (MSW) resonance but also a magnetically induced RSF effect. With the diagram, it is found that four conversions occur in supernovae: two are induced by the RSF effect and two by the pure MSW effect. We also numerically calculate neutrino conversions in supernova matter, using neutrino mixing parameters inferred from recent experimental results and a realistic supernova progenitor model. The results indicate that until 0.5 sec after the core bounce, the RSF-induced ${\overline{\nu }}_e\leftrightarrow {\nu }_{\tau }$ transition occurs efficiently (adiabatic resonance), when ${\mu }_{\nu }\gtrsim {10}^{-12}{\mu }_B{(B}_0/5\mathrm{}\times {10}^9\mathrm{G}{)}^{-1},$ where $B_0$ is the strength of the magnetic field at the surface of iron core. We also evaluate the energy spectrum as a function of ${\mu }_{\nu }{B}_0$ at the super-Kamiokande detector and the Sudbury Neutrino Observatory using the calculated conversion probabilities, and find that the spectral deformation might have the possibility to provide useful information on the neutrino magnetic moment as well as the magnetic field strength in supernovae.

We compute upper limits on cosmic microwave background cross-polarization by cross-correlating the PIQUE and Saskatoon experiments. We also discuss theoretical and practical issues relevant to measuring cross-polarization and illustrate them with simulations of the upcoming BOOMERANG 2002 experiment. We present a method that separates all six polarization power spectra (TT, EE, BB, TE, TB, EB) without any other “leakage” than the familiar EE-BB mixing caused by incomplete sky coverage. Since E and B get mixed, one might expect leakage between TE and TB, between EE and EB and between BB and EB—our method eliminates this by preserving the parity symmetry under which TB and EB are odd and the other four power spectra are even.

We study the possibilities to detect Majorana neutrinos in $\gamma \gamma$ colliders for different center of mass energies. We study the $W^{\pm }{W}^{\pm }{l}_j^{\mp }{l}_k^{\mp }$ ${(l}_j\equiv e,\mu ,\tau )$ final states which are, due to leptonic number violation, a clear signature for an intermediate Majorana neutrino contribution. Such a signal (final dileptons of the same sign) is not possible if the heavy neutrinos are Dirac particles. We present our results for the total cross section as a function of the neutrino mass and center of mass energies.

An analytic analysis of the effects of $\mathrm{CP}$ phases arising from the soft SUSY breaking parameters on the decays $B_{s,d}^0\to l^{+}{l}^{-}$ at large $\tan \beta$ is given. It is found that the phases have a strong effect on the branching ratio and in some regions of the parameter space they can lead to a variation of the branching ratio by as much as 1–2 orders of magnitude. These results have important implications for the discovery of the $B_s^0\to {\mu }^{+}{\mu }^{-}$ signal in run II of the Fermilab Tevatron and further on how the parameter space of SUSY models will be limited once the signal is found.

We derive the general resummed effective Lagrangian for Higgs-mediated flavor-changing neutral-current (FCNC) interactions in the minimal supersymmetric standard model, without resorting to particular assumptions that rely on the squark mass or the quark-Yukawa structure of the theory. In our derivation we also include the possibility of explicit $\mathrm{CP}$ violation through the Cabibbo-Kobayashi-Maskawa mixing matrix and soft supersymmetry-breaking mass terms. The advantages of our resummed FCNC effective Lagrangian are explicitly demonstrated within the context of phenomenologically motivated scenarios. We obtain new testable predictions in the large $\tan \beta$ regime of the theory for CP-conserving and CP-violating observables related to the K- and B-meson systems, such as $\Delta M_{K,B},$ ${\epsilon }_K,$ ${\epsilon }^{\prime }/\epsilon ,$ $\mathcal{B}{(B}_{d,s}\to {\mathcal{l}}^{+}{\mathcal{l}}^{-})$ and their associated leptonic $\mathrm{CP}$ asymmetries. Finally, based on our resummed FCNC effective Lagrangian, we can identify configurations in the soft supersymmetry-breaking parameter space, for which a kind of a Glashow-Iliopoulos-Maiani-cancellation mechanism becomes operative and hence all Higgs-mediated, $\tan \beta$-enhanced effects on K- and B-meson FCNC observables vanish.

The standard model flavor structure can be explained in theories where the fermions are localized on different points in a compact extra dimension. We show that models with two bulk scalars compactified on an orbifold can produce such separations in a natural way. We study the shapes and overlaps of the fermion wave functions. We show that, generically, realistic models of Gaussian overlaps are unnatural since they require very large Yukawa couplings between the fermions and the bulk scalars. We give an example of a five dimensional two scalar model that accounts naturally for the observed quark masses, mixing angles and $\mathrm{CP}$ violation.

I present one-loop perturbative calculations of matching coefficients between matrix elements in continuum regulated QCD and lattice QCD with overlap fermions, with emphasis on a recently proposed variant discretization of the overlap. These fermions have extended (“fat link”) gauge connections. The scale for evaluation of the running coupling constant (in the context of the Lepage-Mackenzie fixing scheme) is also given. A variety of results (for additive mass renormalization, local currents, and some nonpenguin four-fermion operators) for naive, Wilson, clover, and overlap actions are shown.

We calculate the next-to-leading order (NLO) ${\alpha }_s$ corrections to the contributions of the condensates $〈\alpha G^2〉$ and $〈\overline{q}q{〉}^2$ in the current-current correlator of the hybrid current $g\overline{q}\mathrm{}\left(x\right)\mathrm{}{\gamma }_{\nu }{\mathrm{iF}}_{\mu \nu }^a{T}^{a}q\left(x\right)\mathrm{}$ using the external field method in the Feynman gauge. After incorporating these NLO contributions into the Laplace sum rules, the mass of the $J^{\mathrm{PC}}{=1\mathrm{}}^{-+}$ light hybrid meson is recalculated using the QCD sum rule approach. We find that the sum rules exhibit enhanced stability when the NLO ${\alpha }_s$ corrections are included in the sum rule analysis, resulting in a $1^{-+}$ light hybrid meson mass of approximately 1.6 GeV.

We present a general study of exclusive semileptonic decays of heavy ${(B,D,B}_s)$ to light $(\pi ,\rho {,K,K}^{*})$ mesons in the framework of the effective field theory of heavy quarks. The transition matrix elements of these decays can be systematically characterized by a set of wave functions which are independent of the heavy quark mass except for the implicit scale dependence. Form factors for all these decays are calculated consistently within the effective theory framework using the light cone sum rule method at the leading order of the ${1/m}_Q$ expansion. The branching ratios of these decays are evaluated, and the heavy and light flavor symmetry breaking effects are investigated. We also give a comparison of our results and the predictions from other approaches, among which are the relations proposed recently in the framework of large energy effective theory.