Anisotropic lattice fermion actions are investigated with one-loop perturbative calculations aiming at constructing a formulation for a heavy quark with controlled systematic uncertainties. For heavy-light systems at rest an anisotropic lattice with small temporal lattice spacing $a_t$ suppresses the discretization error by a power of $a_t{m}_Q$ for a heavy quark of mass $m_Q.$ We discuss the issue of large discretization errors, which scale as $a_s{m}_Q$ with $a_s$ the spatial lattice spacing. By performing one-loop calculations of the speed-of-light renormalization for several possible lattice actions in the limit of $a_t\to 0,$ we show that one can eliminate the large systematic error on the anisotropic lattice.

We consider two simple covariant models for pions (one with scalar and the other with spin-$\frac{1}{2}$ constituents). Pion generalized parton distributions are derived by integration over the light-cone energy. The model distributions are consistent with all known properties of generalized parton distributions, including positivity. We also construct corresponding double distributions by appealing to the Lorentz invariance of the form factor. These ostensibly constructed double distributions lead to incorrect generalized parton distributions that need not respect the positivity constraints. This inconsistency arises from the ambiguity inherent in defining double distributions in the standard one-component formalism (even in the absence of the Polyakov-Weiss term). We demonstrate that the correct model double distributions can be calculated from nondiagonal matrix elements of twist-two operators.

In this paper we show that in the presence of an antisymmetric tensor B background, Witten’s star algebra for open string fields persists to possess the structure of a direct product of commuting Moyal pairs. The interplay between the noncommutativity due to three-string overlap and that due to the B background is our main concern. In each pair of noncommutative directions parallel to the B background, the Moyal pairs mix string modes in the two directions and are labeled, in addition to a continuous parameter, by two discrete values as well. However, the Moyal parameters are B dependent only for discrete pairs. We have also demonstrated the large-$B$ contraction of the star algebra, with one of the discrete Moyal pairs dropping out and with the other giving rise to the center-of-mass noncommutative function algebra.

The thermal one- and two-graviton Green’s functions are computed using a temporal gauge. In order to handle the extra poles which are present in the propagator, we employ an ambiguity-free technique in the imaginary-time formalism. For temperatures T high compared with the external momentum, we obtain the leading $T^4$ as well as the subleading $T^2$ and $\log \mathrm{}\left(T\right)\mathrm{}$ contributions to the graviton self-energy. The gauge fixing independence of the leading $T^4$ terms as well as the Ward identity relating the self-energy with the one-point function are explicitly verified. We also verify the ’t Hooft identities for the subleading $T^2$ terms and show that the logarithmic part has the same structure as the residue of the ultraviolet pole of the zero temperature graviton self-energy. We explicitly compute the extra terms generated by the prescription poles and verify that they do not change the behavior of the leading and sub-leading contributions from the hard thermal loop region. We discuss the modification of the solutions of the dispersion relations in the graviton plasma induced by the subleading $T^2$ contributions.

We find explicit supergravity solutions which describe branes in the ${\mathrm{AdS}}_3\times {\mathrm{S}}^3$ background. These solutions preserve 8 of the 16 supersymmetries of this background, and are consistent with κ symmetry. These represent new $\frac{1}{2}$ Bogomol’nyi-Prasad-Sommerfield states of string theory.

We critically reexamine the issue of power-law running in models with extra dimensions. The analysis is carried out in the context of a higher-dimensional extension of QED, with the extra dimensions compactified on a torus. It is shown that a naive $\beta$ function, which simply counts the number of modes, depends crucially on the way the thresholds of the Kaluza-Klein modes are crossed. To solve these ambiguities we turn to the vacuum polarization, which, due to its special unitarity properties, guarantees the physical decoupling of the heavy modes. This latter quantity, calculated in the context of dimensional regularization, is used for connecting the low energy gauge coupling with the coupling of the D-dimensional effective field theory. We find that the resulting relation contains only logarithms of the relevant scales, and no power corrections. If, instead, hard cutoffs are used to regularize the theory, one finds power corrections, which could be interpreted as an additional matching between the effective higher-dimensional model and some unknown, more complete theory. The possibility of estimating this matching is examined in the context of a toy model. The general conclusion is that, in the absence of any additional physical principle, the power corrections depend strongly on the details of the underlying theory. Possible consequences of this analysis for gauge coupling unification in theories with extra dimensions are briefly discussed.

It has recently been suggested that the existence of bare strange stars is incompatible with low scale gravity scenarios. It has been claimed that, in such models, high energy neutrinos incident on the surface of a bare strange star would lead to catastrophic black hole growth. We point out that, for the flat large extra dimensional case, the parts of parameter space which give rise to such growth are ruled out by other methods. We then go on to show in detail how black holes evolve in the Randall-Sundrum two brane scenario where the extra dimensions are curved. We find that catastrophic black hole growth does not occur in this situation either. We also present some general expressions for the growth of five dimensional black holes in dense media.

We consider a massive scalar field with arbitrary coupling in ${\mathbf{S}}^1\times {\mathbf{S}}^3$ space, which mimics the thermal expanding Universe, and calculate explicitly all relevant thermodynamical functions in the low- and high-temperature regimes, extending previous analysis of entropy bounds and entropy/energy ratios performed in the conformal case. For high temperatures, new mass-dependent entropy ratios are established which, different from the conformal limit, satisfy Bekenstein’s and Verlinde’s bounds in the physical region.

We use the Lorentzian AdS/CFT prescription to find the poles of the retarded thermal Green’s functions of $\mathcal{N}=4\mathrm{}$ $\mathrm{SU}\left(N\right)\mathrm{}$ supersymmetric Yang-Mills theory in the limit of large N and large ’t Hooft coupling. In the process, we propose a natural definition for quasinormal modes in an asymptotically AdS spacetime, with boundary conditions dictated by the AdS/CFT correspondence. The corresponding frequencies determine the dispersion laws for the quasiparticle excitations in the dual finite-temperature gauge theory. Correlation functions of operators dual to massive scalar, vector and gravitational perturbations in a five-dimensional AdS-Schwarzschild background are considered. We find asymptotic formulas for quasinormal frequencies in the massive scalar and tensor cases, and an exact expression for vector perturbations. In the long-distance, low-frequency limit we recover results of the hydrodynamic approximation to thermal Yang-Mills theory.

A general characterization of lower and upper threshold configurations for two particle reactions is determined under the assumptions that the single particle dispersion relations $E\left(|\mathbf{p}|\right)$ are rotationally invariant and monotonic in $|\mathbf{p}|,$ and that energy and momentum are conserved and additive for multiple particles. It is found that at a threshold the final particle momenta are always parallel and the initial momenta are always antiparallel. The occurrence of new phenomena not occurring in a Lorentz invariant setting, such as upper thresholds and asymmetric pair production thresholds, is explained, and an illustrative example is given.

Recent work has shown that dispersion relations with Planck scale Lorentz violation can produce observable effects at energies many orders of magnitude below the Planck energy M. This opens a window on physics that may reveal quantum gravity phenomena. It has already constrained the possibility of Planck scale Lorentz violation, which is suggested by some approaches to quantum gravity. In this work we carry out a systematic analysis of reaction thresholds, allowing unequal deformation parameters for different particle dispersion relations. The thresholds are found to have some unusual properties compared with standard ones, such as asymmetric momenta for pair creation and upper thresholds. The results are used together with high energy observational data to determine combined constraints. We focus on the case of photons and electrons, using vacuum Čerenkov, photon decay, and photon annihilation processes to determine order unity constraints on the parameters controlling $O(E/M)\mathrm{}$ Lorentz violation. Interesting constraints for protons (with photons or pions) are obtained even at $O\left({\mathrm{}(E/M)\mathrm{}}^2\right),$ using the absence of vacuum Čerenkov and the observed GZK cutoff for ultrahigh energy cosmic rays. A strong Čerenkov limit using atmospheric PeV neutrinos is possible for $O(E/M)\mathrm{}$ deformations provided the rate is high enough. If detected, ultrahigh energy cosmological neutrinos might yield limits at or even beyond $O\left({\mathrm{}(E/M)\mathrm{}}^2\right).$

Weak gravitational lensing by an intervening large-scale structure induces a distinct signature in the cosmic microwave background (CMB) that can be used to reconstruct the weak-lensing displacement map. Estimators for individual Fourier modes of this map can be combined to produce an estimator for the lensing-potential power spectrum. The naive estimator for this quantity will be biased upwards by the uncertainty associated with reconstructing individual modes; we present an iterative scheme for removing this bias. The variance and covariance of the lensing-potential power spectrum estimator are calculated and evaluated numerically in a $\Lambda \mathrm{CDM}$ universe for Planck and future polarization-sensitive CMB experiments.

We discuss the baseline optical configuration for the Laser Interferometer Space Antenna (LISA) mission, in which the lasers are not free-running, but rather one of them is used as the main frequency reference generator (the master) and the remaining five as slaves, these being phase-locked to the master (the master-slave configuration). Under the condition that the frequency fluctuations due to the optical transponders can be made negligible with respect to the secondary LISA noise sources (mainly proof-mass and shot noises), we show that the entire space of interferometric combinations LISA can generate when operated with six independent lasers (the one-way method) can also be constructed with the master-slave system design. The corresponding hardware trade-off analysis for these two optical designs is presented, which indicates that the two sets of systems needed for implementing the one-way method, and the master-slave configuration, are essentially identical. Either operational mode could therefore be implemented without major implications on the hardware configuration. We then derive the required accuracies of armlength knowledge, time synchronization of the onboard clocks, sampling times and time-shifts needed for effectively implementing time-delay interferometry for LISA. We find that an armlength accuracy of about 16 meters, a synchronization accuracy of about 50 ns, and the time jitter due to a presently existing space qualified clock will allow the suppression of the frequency fluctuations of the lasers below to the level identified by the secondary noise sources. A new procedure for sampling the data in such a way to avoid the problem of having time shifts that are not integer multiples of the sampling time is also introduced, addressing one of the concerns about the implementation of time-delay interferometry.

I derive a class of functions unifying all singular limits for the emission of a given number of soft or collinear gluons in tree-level gauge-theory amplitudes. Each function is a generalization of the single-emission antenna function of my earlier paper. The helicity-summed squares of these functions are thus also generalizations to multiple singular emission of the Catani-Seymour dipole factorization function.

The spontaneous symmetry breaking of rotational $O\left(N\right)\mathrm{}$ symmetry in noncommutative field theory is investigated in a 2+1 dimensional model of scalar fields coupled through a combination of quartic and sextuple self-interactions. There are five possible orderings of the fields in the sextuple interaction and two for the quartic interaction. At one loop, we prove that for some choices of these orderings there is the absence of IR-UV mixing and the appearance of massless excitations. A supersymmetric extension of the model is also studied. Supersymmetry puts additional constraints on the couplings but for any given N there is a Moyal ordering of the superfields for which the requirement for the existence of Goldstone bosons is satisfied. For some ordering and when $\overrightarrow{N}\infty$ we find evidence that the model is renormalizable to all orders in perturbation theory. We also consider a generic chiral model in $3+1$ dimensions whose superpotential is invariant under local gauge transformations. We find that for any value of N there is no one loop correction to the pion mass and that, at two loops, there are no pion mass corrections for slowly varying superfields so that the Goldstone theorem holds true. We also find a new purely noncommutative coupling which gives contributions starting at order $N-2$ loops.

We present analytical expressions for the Fourier analogue of the cosmic microwave background three-point and four-point correlation functions, the spatial bispectrum and trispectrum, of the Ostriker-Vishniac effect in the linear and mildly nonlinear regime. Through this systematic study, we illustrate a technique to tackle the calculation of such statistics making use of the effects of its small-angle and vectorlike properties through the Limber approximation. Finally we discuss its configuration dependence and detectability in the context of Gaussian theories for the currently favored flat $\Lambda$CDM cosmology.

By making full use of the field theoretical nature of the chiral quark soliton model, we demonstrate that the nonvanishing quark condensate as a signal of the spontaneous chiral symmetry breaking of the QCD vacuum brings about a delta-function singularity at $x=0\mathrm{}$ in the chirally odd twist-3 distribution $e\left(x\right)\mathrm{}$ of the nucleon. This singularity in $e\left(x\right),$ which would be observed as a sizable violation of the 1st moment sum rule, is then interpreted as giving a very rare case that the nontrivial vacuum structure of QCD manifests in an observable of a localized QCD excitation, i.e., the nucleon.

The chirally-odd twist-3 nucleon distribution $e^a\mathrm{}\left(x\right)\mathrm{}$ is studied in the large-$N_c$ limit in the framework of the chiral quark-soliton model at a low normalization point of about $0.6\mathrm{GeV}.$ The remarkable result is that in the model $e^a\mathrm{}\left(x\right)\mathrm{}$ contains a $\delta$-function-type singularity at $x=0.\mathrm{}$ The regular part of $e^a\mathrm{}\left(x\right)\mathrm{}$ is found to be sizable at the low scale of the model and in qualitative agreement with bag model calculations.

We present a procedure that allows the construction of the metric perturbations and electromagnetic four-potential, for gravitational and electromagnetic perturbations produced by sources in Kerr spacetime. This may include, for example, the perturbations produced by a point particle or an extended object moving in orbit around a Kerr black hole. The construction is carried out in the frequency domain. Previously, Chrzanowski derived the vacuum metric perturbations and electromagnetic four-potential by applying a differential operator to a certain potential $\Psi .$ Here we construct $\Psi$ for inhomogeneous perturbations, thereby allowing the application of Chrzanowski’s method. We address this problem in two stages: First, for vacuum perturbations (i.e. pure gravitational or electromagnetic waves), we construct the potential from the modes of the Weyl scalars ${\psi }_0$ or ${\phi }_0.$ Second, for perturbations produced by sources, we express $\Psi$ in terms of the mode functions of the source, i.e. the energy-momentum tensor $T_{\alpha \beta }$ or the electromagnetic current vector $J_{\alpha }.$

We study string-gas cosmology in dilaton gravity, inspired by the fact that it naturally arises in a string theory context. Our main interest is the thermodynamical treatment of the ideal string-gas and the resulting implications for the cosmology. Within an adiabatic approximation, thermodynamical equilibrium and a small, toroidal universe as initial conditions, we numerically solve the corresponding equations of motions in two different regimes describing the string-gas thermodynamics: (i) the Hagedorn regime, with a single scale factor, and (ii) an almost-radiation dominated regime, which includes the leading corrections due to the lightest Kaluza-Klein and winding modes, with two scale factors. The scale factor in the Hagedorn regime exhibits very slow time evolution with nearly constant energy and negligible pressure. By contrast, in case (ii) we find interesting cosmological solutions where the large dimensions continue to expand and the small ones are kept undetectably small.