We study the role of large clusters of center vortices in producing confinement in $3\mathrm{D}$ $Z_2$ gauge theory. First, we modify each configuration of a Monte Carlo–generated ensemble in the confined phase by removing the largest cluster of center vortices, and show that the ensemble thus obtained does not confine. Conversely, we show that by removing all of the small clusters of center vortices and leaving the largest one only, confinement is preserved, albeit with a string tension significantly smaller than the original one. Remarkably, also the string corrections due to the quantum fluctuations of the confining flux tube are preserved by this transformation.

Contributions to the bound-state dynamics of fermions in local quantum field theory from the region of large relative momenta of the constituent particles are studied and compared in two different approaches. The first approach is conventionally developed in terms of bare fermions, a Tamm-Dancoff truncation on the particle number, and a momentum-space cutoff that requires counterterms in the Fock-space Hamiltonian. The second approach to the same theory deals with bound states of effective fermions, the latter being derived from a suitable renormalization-group procedure. An example of two-fermion bound states in Yukawa theory, quantized in the light-front form of dynamics, is discussed in detail. The large-momentum region leads to a buildup of overlapping divergences in the bare Tamm-Dancoff approach, while the effective two-fermion dynamics is little influenced by the large-momentum region. This is illustrated by numerical estimates of the large-momentum contributions for coupling constants on the order of between 0.01 and 1, which is relevant for quarks.

We study lepton flavor violating signals at a future $e^{+}{e}^{-}$ linear collider within the general minimal supersymmetric standard model (MSSM), allowing for the most general flavor structure. There exists a large region in parameter space with large signals being consistent with present experimental bounds on rare lepton decays. We include all possible signals from slepton and sneutrino production and their decays as well as from neutralino and chargino decays. We also consider the background from the standard model and the MSSM. We find that in general the signature $e\tau E_T$ is the most pronounced one.

Using quenched reduction, we propose a method for the numerical calculation of meson correlation functions in the planar limit of QCD. General features of the approach are outlined, and an example is given in the context of two-dimensional QCD.

Assuming the existence of a dS/conformal field theory correspondence we study the holograms of sources moving along geodesics in the bulk by calculating the one point functions they induce in the boundary theory. In analogy with a similar study of uniformly accelerated sources in AdS spacetime, we argue that comoving geodesic observers correspond to a coordinate system on the boundary in which the one point function is constant. For ${\mathrm{dS}}_3$ we show that the conformal transformations on the boundary that achieve this, when continued suitably to Lorentzian signature, induce nontrivial Bogoliubov transformations between modes, leading to a thermal spectrum. This may be regarded as a holographic signature of thermality detected by bulk geodesic observers.

The effective equations of motion for a point charged particle taking into account the radiation reaction are considered in various space-time dimensions. The divergences stemming from the pointness of the particle are studied and an effective renormalization procedure is proposed encompassing uniformly the cases of all even dimensions. It is shown that in any dimension the classical electrodynamics is a renormalizable theory if not multiplicatively beyond $d=4.\mathrm{}$ For the cases of three and six dimensions the covariant analogues of the Lorentz-Dirac equation are explicitly derived.

We discuss the radiation reaction problem for an electric charge moving in flat space-time of arbitrary dimensions. It is shown that four is the unique dimension where a local differential equation exists accounting for the radiation reaction and admitting a consistent mass renormalization (the Lorentz-Dirac equation). In odd dimensions Huygens’s principle does not hold, and, as a result, the radiation reaction force depends on the whole past history of a charge (radiative tail). We show that the divergence in the tail integral can be removed by the mass renormalization only in the $2+1$ theory. In even dimensions higher than four, divergences cannot be removed by the mass renormalization.

In this paper a family of nonsingular cylindrical perfect fluid cosmologies is derived. The equation of state corresponds to a stiff fluid. The family depends on two independent functions under very simple conditions. A sufficient condition for geodesic completeness is provided.

We analyze the evolution of energy density fluctuations in cosmological scenarios with a mixture of cold dark matter and quintessence, in which the quintessence field is modeled by a constant equation of state. We obtain analytic expressions for the time evolution of the quintessence perturbations in models with light fields. The fluctuations behave analogously to a driven harmonic oscillator, where the driving term arises from the inhomogeneities in the surrounding cosmological fluid. We demonstrate that the homogeneous solution, determined by the initial conditions, is completely subdominant to the inhomogeneous solution for physically realistic scenarios. Thus we show that the cosmic microwave background anisotropy predicted for such models is highly insensitive to the initial conditions in the quintessence field.

Mass spectra of baryons consisting of two heavy $(b$ or $c)$ and one light quark are calculated in the framework of the relativistic quark model. The light-quark–heavy-diquark structure of the baryon is assumed. Under this assumption the ground and excited states of both the diquark and quark-diquark bound system are considered. The quark-diquark potential is constructed. The light quark is treated completely relativistically, while the expansion in the inverse heavy quark mass is used revealing the close similarity with the mass spectra of B and D mesons. We find that the relativistic treatment of the light quark plays an important role. The level inversion of the p-wave excitations of the light quark in doubly heavy baryons is discussed.

A recent numerical study by A. D. Dolgov, S. H. Hansen, S. Pastor, S. T. Petcov, G. G. Raffelt, and D. V. Semikoz (DHPPRS) [Nucl. Phys. B632, 363 (2002)] found that complete or partial equilibrium between all active neutrino flavors can be achieved before the big bang nucleosynthesis epoch via flavor oscillations, if the oscillation parameters are those inferred from the atmospheric and solar neutrino data, and, in some cases, if ${\theta }_{13}$ is also sizable. As such, cosmological constraints on the electron neutrino-antineutrino asymmetry are now applicable in all three neutrino sectors. In the present work, we provide an analytical treatment of the scenarios considered in DHPPRS, and demonstrate that their results are stable even for very large initial asymmetries. The equilibration mechanism can be understood in terms of a Mikheyev-Smirnov-Wolfenstein-like effect for a maximally mixed and effectively monochromatic system. We also comment on the DHPPRS’s choices of mixing parameters, and their handling of collisional effects, both of which could impinge on the extent of flavor equilibrium.

The squared mass of a complex scalar field is turned dynamically negative by its $O\left(2\right)\mathrm{}$-invariant coupling to a real field slowly rolling down in a quadratic potential. The emergence of gapless excitations is studied in real time simulations after spinodal instability occurs. Careful tests demonstrate that the Goldstone modes appear almost instantly after the symmetry breaking is over, much before thermal equilibrium is established.

$\mathcal{N}=2\mathrm{}$ supersymmetric QED with several flavors admits multiple, static BPS domain wall solutions. We determine the explicit two-kink metric and examine the dynamics of colliding domain walls. The multikink metric has a toric Kähler structure and we reduce the Kähler potential to quadrature. In the second part of this paper, we consider semilocal vortices on $\mathbf{R}\times {\mathbf{S}}^1.$ We argue that, in the presence of a suitable Wilson line, the vortices separate into domain wall constituents. These play the role of fractional instantons in two-dimensional gauge theories and sigma models.

Perturbation theory of rotating black holes is usually described in terms of Weyl scalars ${\psi }_4$ and ${\psi }_0,$ which each satisfy Teukolsky’s complex master wave equation and respectively represent outgoing and ingoing radiation. On the other hand metric perturbations of a Kerr hole can be described in terms of (Hertz-like) potentials $\Psi$ in outgoing or ingoing radiation gauges. In this paper we relate these potentials to what one actually computes in perturbation theory, i.e. ${\psi }_4$ and ${\psi }_0.$ We explicitly construct these relations in the nonrotating limit, preparatory to devising a corresponding approach for building up the perturbed spacetime of a rotating black hole. We discuss the application of our procedure to second order perturbation theory and to the study of radiation reaction effects for a particle orbiting a massive black hole.

We study the consistency of orbifold field theories and clarify to what extent the condition of having an anomaly-free spectrum of zero modes is sufficient to guarantee it. Preservation of gauge invariance at the quantum level is possible, although at the price, in general, of introducing operators that break the 5D local parity. These operators are, however, perfectly consistent with the orbifold projection. We also clarify the relation between localized Fayet-Iliopoulos (FI) terms and anomalies. These terms can be consistently added, breaking neither local supersymmetry nor gauge symmetry. In the framework of supergravity the localized FI term arises as the boundary completion of a bulk interaction term: given the bulk Lagrangian the FI is fixed by gauge invariance.

The embedding of a thick de Sitter 3-brane into a five-dimensional bulk is studied, assuming a scalar field with a potential is present in the bulk. A class of solutions is found in closed form that can represent a thick de Sitter 3-brane interpolating either between two dynamical black holes with an $R\times S_4$ topology or between two Rindler-like spacetimes with an $R_2\times S_3$ topology. The gravitational field is localized in a small region near the center of the 3-brane. The analysis of graviton fluctuations shows that a zero mode exists and separates itself from a set of continuous modes by a mass gap. The existence of such a mass gap is shown to be universal. The scalar perturbations are also studied and shown to be stable.

In the context of brane-world theories, the production cross section for black holes may be greatly enhanced. Such black holes can in principle lead to detectable signals via their Hawking evaporation to brane-localized modes. We calculate, in the semiclassical approximation, the leading corrections to the energy spectrum (the greybody factors) for decay into scalar fields, as a function of the number of toroidally compactified extra dimensions, and partial wave number.

Building on general formulas obtained from the approximate renormalized effective action, the approximate stress-energy tensor of the quantized massive scalar field with arbitrary curvature coupling in the spacetime of a charged black hole that is the solution of the coupled equations of nonlinear electrodynamics and general relativity is constructed and analyzed. It is shown that, in a few limiting cases, the analytical expressions relating the obtained tensor to the general renormalized stress-energy tensor evaluated in the geometry of the Reissner-Nordström black hole can be derived. A detailed numerical analysis with special emphasis put on minimal coupling is presented, and the results are compared with those obtained earlier for a conformally coupled field. Some novel features of the renormalized stress-energy tensor are discussed.

The Immirzi ambiguity arises in loop quantum gravity when geometric operators are represented in terms of different connections that are related by means of an extended Wick transform. We analyze the action of this transform in gravity coupled with matter fields and discuss its analogy with the Wick rotation on which the Thiemann transform between Euclidean and Lorentzian gravity is based. In addition, we prove that the effect of this extended Wick transform is equivalent to a constant scale transformation as far as the symplectic structure and kinematical constraints are concerned. This equivalence is broken in the dynamical evolution. Our results are applied to the discussion of the black hole entropy in the limit of large horizon areas. We first argue that, since the entropy calculation is performed for horizons of fixed constant area, one might in principle choose an Immirzi parameter that depends on this quantity. This would spoil the linearity with the area in the entropy formula. We then show that the Immirzi parameter appears as a constant scaling in all the steps where dynamical information plays a relevant role in the entropy calculation. This fact, together with the kinematical equivalence of the Immirzi ambiguity with a change of scale, is used to preclude the potential nonlinearity of the entropy on physical grounds.

We consider approaches to cosmological parameter estimation in the inflationary cosmology, focusing on the required accuracy of the initial power spectra. Parametrizing the spectra, for example by power laws, is well suited to testing the inflationary paradigm but will only correctly estimate cosmological parameters if the parametrization is sufficiently accurate, and we investigate conditions under which this is achieved both for present data and for upcoming satellite data. If inflation is favored, reliable estimation of its physical parameters requires an alternative approach adopting its detailed predictions. For slow-roll inflation, we investigate the accuracy of the predicted spectra at first and second order in the slow-roll expansion (presenting the complete second-order corrections for the tensors for the first time). We find that, within the presently allowed parameter space, there are regions where it will be necessary to include second-order corrections to reach the accuracy requirements of MAP and Planck satellite data. We end by proposing a data analysis pipeline appropriate for testing inflation and for a cosmological parameter estimation from high-precision data.