The recently proposed nonlocal and nonperturbative late time behavior of the heat kernel is generalized to curved spacetimes. Heat kernel trace asymptotics is dominated by two terms, one of which represents a trivial covariantization of the flat-space result and another one is given by the Gibbons-Hawking integral over asymptotically flat infinity. Nonlocal terms of the effective action generated by this asymptotics might underly long-distance modifications of the Einstein theory motivated by the cosmological constant problem. New mechanisms of the cosmological constant induced by infrared effects of matter and graviton loops are briefly discussed.

We apply the path-integral formalism to compute the anomalies in general orbifold gauge theories (including possible nontrivial Scherk-Schwarz boundary conditions) where a gauge group $\mathcal{G}$ is broken down to subgroups ${\mathcal{H}}_f$ at the fixed points ${y=y}_f.$ Bulk and localized anomalies, proportional to $\delta \left(y-y_f\right),$ do generically appear from matter propagating in the bulk. The anomaly zero mode that survives in the four-dimensional effective theory should be canceled by localized fermions [except possibly for mixed $U\left(1\right)\mathrm{}$ anomalies]. We examine in detail the possibility of canceling localized anomalies by the Green-Schwarz mechanism involving two- and four-forms in the bulk. The four-form can only cancel anomalies which do not survive in the 4D effective theory: they are called globally vanishing anomalies. The two-form may cancel a specific class of mixed $U\left(1\right)\mathrm{}$ anomalies. Only if these anomalies are present in the 4D theory does this mechanism spontaneously break the $U\left(1\right)\mathrm{}$ symmetry. The examples of five- and six-dimensional $Z_N$ orbifolds are considered in great detail. In five dimensions the Green-Schwarz four-form has no physical degrees of freedom and is equivalent to canceling anomalies by a Chern-Simons term. In all other cases, the Green-Schwarz forms have some physical degrees of freedom and leave some nonrenormalizable interactions in the low energy effective theory. In general, localized anomaly cancellation imposes strong constraints on model building.

This work establishes critical phenomena in the topological transition of black hole coalescence. We describe and validate a computational front tracking event horizon solver, developed for generic studies of the black hole coalescence problem. We then apply this to the Kastor-Traschen axisymmetric analytic solution of the extremal Maxwell-Einstein black hole merger with a cosmological constant. The surprising result of this computational analysis is a power law scaling of the minimal throat proportional to time. The minimal throat connecting the two holes obeys this power law during a short time immediately at the beginning of merger. We also confirm the behavior analytically. Thus, at least in one axisymmetric situation a critical phenomenon exists. We give arguments for a broader universality class than the restricted requirements of the Kastor-Traschen solution.

Using the improved lattice gauge field Hamiltonian and the truncated eigenvalue equation method, we compute the vacuum wave function and mass gap of three-dimensional SU(2) gauge field theory. Our results show that the improved theory leads to a significant reduction of violation of scaling, that is, using the improved lattice gauge field Hamiltonian, the calculations can be carried out up to a much weaker coupling region than using the unimproved one, with good scaling behavior.

We analyze color superconductivity of one massive flavor quark matter at moderate baryon density with a spin-zero color-sextet condensate. The most general Higgs-type ground-state expectation value of the order parameter implies complete breakdown of the $\mathrm{SU}\left(3\right)\mathrm{}\times U\left(1\right)\mathrm{}$ symmetry. However, both the conventional fourth-order polynomial effective bosonic description and the Nambu–Jona-Lasinio–type fermionic description in the mean-field approximation favor an enhanced $\mathrm{SO}\left(3\right)\mathrm{}$ symmetry of the ground state. We ascribe this finding to the failure of the mean-field approximation and propose that a more sophisticated technique is needed.

The role of higher meson resonances with spin 1 and 2 is investigated quantitatively in the decay processes of $\overrightarrow{\rho }{\pi }^0{\pi }^0\gamma$ and $\overrightarrow{\omega }{\pi }^0{\pi }^0\gamma .$ Among the higher resonances, we find that the $f_2\mathrm{}\left(1270\right)\mathrm{}$ tensor meson can give a nontrivial contribution especially to the $\overrightarrow{\omega }{\pi }^0{\pi }^0\gamma$ decay process. When the $f_2$ contribution is combined with the processes involving the vector and scalar meson intermediate states, good agreement with the recent measurements is achieved for both decays. The effect of the $f_2\mathrm{}\left(1270\right)\mathrm{}$ is found to be sizable at intermediate photon energies and may be verified by precise measurements of the recoil photon spectrum of the $\overrightarrow{\omega }{\pi }^0{\pi }^0\gamma$ decay. The dependence of the decay widths on various models for $\rho -\omega$ mixing in the literature is also investigated.

The production of three jets in hadron-hadron collisions is the first complex process which allows us to define a branch of variables in order to make more precise measurements of the strong coupling and the parton distribution function of the proton. This process is also suitable for studying the geometrical properties of the hadronic final state at hadron colliders. This requires a next-to-leading order prediction of the three-jet observables. In this paper we describe the theoretical formalism of such a calculation with sufficient detail. We use the dipole method to construct a Monte Carlo program for calculating three-jet observables at next-to-leading order accuracy. We present a theoretical prediction for inclusive and exclusive cross sections and for some relevant event shape variables such as the transverse thrust, transverse jet broadening, and $E_{t3\mathrm{}}$ variable.

We construct the higher twist structure functions that describe inclusive b hadron decays in regions of phase space where the hadronic decay products carry high energy but have low invariant mass. We show that, for B meson decays, there are four new nonvanishing matrix elements of nonlocal operators. We show that to subleading twist these decays are parametrized in terms of four functions. We compute the tree-level matching for a general heavy-to-light current and apply it to $\overline{B}\to X_s\gamma .$ Using a simple model for these functions we estimate the subleading twist contributions to this decay.

We study the decays of ${\tau }^{-}\to {\nu }_{\tau }{P}^{-}\gamma (P={\pi }^{-}{,K}^{-})$ in the light front quark model. We calculate the form factors and use them to evaluate the decay widths. We find that, in the standard model, the decay widths are $1.62\times {10}^{-2}(3.86\mathrm{}\times {10}^{-3}){\Gamma }_{{\tau }^{-}\to {\nu }_{\tau }{\pi }^{-}}$ and $1.91\times {10}^{-3}(5.38\mathrm{}\times {10}^{-4}){\Gamma }_{{\tau }^{-}\to {\nu }_{\tau }{K}^{-}}$ with the cuts of $E_{\gamma }=50\mathrm{}\left(400\right)\mathrm{}\mathrm{MeV}$ and $t_0=800\mathrm{}\left(1200\right)\mathrm{}\mathrm{MeV}$ for ${\tau }^{-}\to {\nu }_{\tau }{\pi }^{-}\gamma$ and ${\tau }^{-}\to {\nu }_{\tau }{K}^{-}\gamma ,$ respectively. We also show that, with including the radiative decay widths, the experimental rate for ${\tau }^{-}\to {\nu }_{\tau }{P}^{-}$ can be explained.

We study the worldvolume supersymmetries of $M2\mathrm{}$ branes in the maximally supersymmetric plane wave background of M theory. For certain embeddings the standard probe analysis indicates that the worldvolume theory has less than 16 supersymmetries. We show that at the quadratic level the worldvolume theory admits additional linearly realized supersymmetries, and that the spectra of the branes are organized into multiplets of these symmetries. We find, however, that these supersymmetries are not respected by worldvolume interactions. Our analysis was motivated by recent work showing that D branes in the maximally supersymmetric plane wave background of type IIB string theory admit supersymmetries beyond those of the probe analysis. The construction of the additional supercharges in this case was specific to a string worldsheet that is a strip and the present results suggest that string interactions do not preserve these symmetries.

A coexistent phase of spin polarization and color superconductivity in high-density QCD is investigated using a self-consistent mean-field method at zero temperature. The axial-vector self-energy stemming from the Fock exchange term of the one-gluon-exchange interaction has a central role in causing spin polarization. The magnitude of spin polarization is determined by the coupled Schwinger-Dyson equations with a superconducting gap function. As a significant feature, the Fermi surface is deformed by the axial-vector self-energy and then rotation symmetry is spontaneously broken down. The gap function results in being anisotropic in the momentum space in accordance with the deformation. As a result of numerical calculations, it is found that spin polarization barely conflicts with color superconductivity, but almost coexists with it.

The Rayleigh criterion is used to study the stability of circular orbits of particles moving around static black holes surrounded by different axially symmetric structures with reflection symmetry, such as disks, rings, and halos. We consider three models of disks, one of infinite extension and two finite, and one model of rings. The halos are represented by external quadrupole moments (either oblate or prolate). Internal quadrupole perturbations (oblate and prolate) are also considered. For this class of disks the counterrotation hypothesis implies that the stability of the disks is equivalent to the stability of test particles. The stability of Newtonian systems is also considered and compared with the equivalent relativistic situation. We find that the general relativistic dynamics favors the formation of rings.

Wheeler asked how one might derive the Einstein-Hamilton-Jacobi equation from plausible first principles without any use of the Einstein field equations themselves. In addition to Hojman, Kuchař and Teitelboim’s “seventh route to relativity” partial answer to this, there is now a “3-space” partial answer due to Barbour, Foster and Ó Murchadha (BFÓ) which principally differs in that general covariance is no longer presupposed. BFÓ’s formulation of the 3-space approach is based on best-matched actions such as the lapse-eliminated Baierlein-Sharp-Wheeler (BSW) action of general relativity (GR). These give rise to several branches of gravitational theories including GR on superspace and a theory of gravity on conformal superspace. This paper investigates the 3-space approach further, motivated both by the hierarchies of increasingly well-defined and weakened simplicity postulates present in all routes to relativity, and by the requirement that all the known fundamental matter fields be included. We further the study of configuration spaces of gravity-matter systems upon which BFÓ’s formulation leans. We note that in further developments the lapse-eliminated BSW actions used by BFÓ become impractical and require generalization. We circumvent many of these problems by the equivalent use of lapse-uneliminated actions, which furthermore permit us to interpret BFÓ’s formulation within Kuchař’s generally covariant hypersurface framework. This viewpoint provides alternative reasons to BFÓ’s as to why the inclusion of bosonic fields in the 3-space approach gives rise to minimally coupled scalar fields, electromagnetism and Yang-Mills theory. This viewpoint also permits us to quickly exhibit further GR-matter theories admitted by the 3-space formulation. In particular, we show that the spin-$\frac{1}{2}$ fermions of the theories of Dirac, Maxwell-Dirac and Yang-Mills-Dirac, all coupled to GR, are admitted by the generalized 3-space formulation we present. Thus all the known fundamental matter fields can be accommodated. This corresponds to being able to pick actions for all these theories which have less kinematics than suggested by the generally covariant hypersurface framework. For all these theories, Wheeler’s thin sandwich conjecture may be posed, rendering them timeless in Barbour’s sense.

We provide simple examples of the generation of complex mass terms and hence CP violation through dimensional reduction. This CP violation originates in the “Hosotani mechanism,” relying on nontrivial Wilson lines, assumed to appear in the dimensional reduction.

We calculate the electric charge radii of the $\mathrm{SU}\left(3\right)\mathrm{}$ pseudoscalar mesons and the $\mathrm{SU}\left(3\right)\mathrm{}$ octet baryons in quenched and partially quenched chiral perturbation theory. We work in the isospin limit, up to next-to-leading order in the chiral expansion, and to leading order in the heavy baryon expansion. The results are necessary for the extrapolation of future lattice calculations of meson and baryon charge radii. We also derive expressions for the nucleon and pion charge radii in $\mathrm{SU}\left(2\right)\mathrm{}$ flavor away from the isospin limit.

Boundary states that preserve supersymmetry are constructed for fractional D strings with traveling waves on a ${\mathbf{C}}^3/{\mathbf{Z}}_2\times {\mathbf{Z}}_2$ orbifold. The gravitational radiation emitted between two D strings with antiparallel traveling waves is calculated.

In models of universal extra dimensions, gravity and all standard model fields propagate in the extra dimensions. Previous studies of such models have concentrated on the Kaluza-Klein (KK) partners of standard model particles. Here we determine the properties of the KK gravitons and explore their cosmological implications. We find the lifetimes of decays to KK gravitons, of relevance for the viability of KK gravitons as dark matter. We then discuss the primordial production of KK gravitons after reheating. The existence of a tower of KK graviton states makes such production extremely efficient: for reheat temperature $T_{\mathrm{RH}}$ and d extra dimensions, the energy density stored in gravitons scales as $T_{\mathrm{RH}}^{2+3d/2}.$ Overclosure and big bang nucleosynthesis therefore stringently constrain $T_{\mathrm{RH}}$ in all universal extra dimension scenarios. At the same time, there is a window of reheat temperatures low enough to avoid these constraints and high enough to generate the desired thermal relic density for KK weakly interacting massive particle (WIMP) and superWIMP dark matter.

We present a method for the introduction of small-scale structure into strings constructed from products of rotation matrices. We use this method to illustrate a range of possibilities for the shape of cusps that depends on the properties of the small-scale structure. We further argue that the presence of structure at cusps under most circumstances leads to the formation of loops at the size of the smallest scales. On the other hand we show that the gravitational waveform of a cusp remains generally unchanged; the primary effect of small-scale structure is to smooth out the sharp waveform emitted in the direction of cusp motion.

A functional method is discussed, where the quantum fluctuations of a theory are controlled by a mass parameter and the evolution of the theory with this parameter is connected to its renormalization. It is found, in the framework of the gradient expansion, that the coupling constant of an $N=1\mathrm{}$ Wess-Zumino theory in $2+1$ dimensions does not get quantum corrections.

We analyze the possibility of nonperturbative renormalizability of gauge theories in $D>\mathrm{}4\mathrm{}$ dimensions. We develop a scenario, based on Weinberg’s idea of asymptotic safety, that allows for renormalizability in extra dimensions owing to a non-Gaussian ultraviolet stable fixed point. Our scenario predicts a critical dimension $D_{\mathrm{cr}}$ beyond which the UV fixed point vanishes, such that renormalizability is possible for $D<~D_{\mathrm{cr}}.$ Within the framework of exact renormalization group equations, the critical dimension for various $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ gauge theories can be computed to lie near five dimensions: $5\lesssim D_{\mathrm{cr}}<6.\mathrm{}$ Therefore, our results exclude nonperturbative renormalizability of gauge theories in $D=6\mathrm{}$ and higher dimensions.