International Journal of Modern Physics A

I review three attempts to explain the small value of the cosmological constant, and their connection to supersymmetry breaking. They are The String Landscape, Supersymmetric Large Extra Dimensions (SLED), and the Holographic Space–time Formalism invented by Fischler and myself.

Black holes are probably among the most fascinating objects populating our universe. Their characteristic features found within general relativity, encompassing space–time singularities, event horizons, and black hole thermodynamics, provide a rich testing ground for quantum gravity ideas. We review the status of black holes within a particular proposal for quantum gravity, Weinberg's asymptotic safety program. Starting from a brief survey of the effective average action and scale setting procedures, an improved quantum picture of the black hole is developed. The Schwarzschild black hole and its generalizations including angular momenta, higher-derivative corrections and the implications of extra dimensions are discussed in detail. In addition, the quantum singularity emerging for the inclusion of a cosmological constant is elucidated and linked to the phenomenon of a dynamical dimensional reduction of space–time.

We summarize and expand our investigations concerning the soft graviton effects on microscopic matter dynamics in de Sitter space. The physical couplings receive IR logarithmic corrections which are sensitive to the IR cutoff at the one-loop level. The scale invariant spectrum in the gravitational propagator at the super-horizon scale is the source of the de Sitter symmetry breaking. The quartic scalar, Yukawa and gauge couplings become time dependent and diminish with time. In contrast, the Newton's constant increases with time. We clarify the physical mechanism behind these effects in terms of the conformal mode dynamics in analogy with 2d quantum gravity. We show that they are the inevitable consequence of the general covariance and lead to gauge invariant predictions. We construct a simple model in which the cosmological constant is self-tuned to vanish due to UV–IR mixing effect. We also discuss phenomenological implications such as decaying Dark Energy and SUSY breaking at the inflation era. The quantum effect alters the classical slow roll picture in general, if the tensor-to-scalar ratio r is as small as 0.01.

In the course of a nonequilibrium continuous phase transition, the dynamics ceases to be adiabatic in the vicinity of the critical point as a result of the critical slowing down (the divergence of the relaxation time in the neighborhood of the critical point). This enforces a local choice of the broken symmetry and can lead to the formation of topological defects. The Kibble–Zurek mechanism (KZM) was developed to describe the associated nonequilibrium dynamics and to estimate the density of defects as a function of the quench rate through the transition. During recent years, several new experiments investigated the formation of defects in phase transitions induced by a quench both in classical and quantum mechanical systems. At the same time, some established results were called into question. We review and analyze the Kibble–Zurek mechanism focusing in particular on this surge of activity, and suggest possible directions for further progress.

Low-energy Lorentz-invariant quantities could receive contributions from a fundamental theory producing small Lorentz-violating effects. Within the Lorentz-violating extension of quantum electrodynamics, we investigate, perturbatively, the contributions to the one-loop ffγ vertex from the CPT-violating axial coupling of a vector background field to fermions. We find that the resulting vertex function has a larger set of Lorentz structures than the one characterizing the usual, Lorentz-invariant, parametrization of the ffγ vertex. We prove gauge invariance of the resulting one-loop expression through a set of gauge invariant nonrenormalizable operators introducing new-physics effects at the first- and second-orders in Lorentz-violation, and which generate tree-level contributions to the ffγ vertex. Whereas loop contributions involving parameters that violate Lorentz-invariance at the first-order are CPT-odd, those arising at the second-order are CPT-even, so that contributions to low-energy physics are restricted to emerge for the first time at the second-order. In this context, we derive a contribution to anomalous magnetic moment (AMM) of fermions, which we use to set a bound on Lorentz-violation.

Gravitating monopoles and dyons in Einstein–Yang–Mills (EYM) or Einstein–Yang–Mills–Higgs (EYMH) systems have been extensively studied for various curved space–times, including those of black holes. We construct dyonic solutions of the EYMH theory in Vaidya space–time using a set of generalized Julia–Zee ansatz for the fields. It is found that the dyonic charge is static in nature and it does not contribute to the energy of the null dust.

We reconsider the thermal scalar Casimir effect for p-dimensional rectangular cavity inside (D+1)-dimensional Minkowski space–time and clarify the ambiguity in the regularization of the temperature-dependent part of the free energy. We derive rigorously the regularization of the temperature-dependent part of the free energy by making use of the Abel–Plana formula repeatedly and get the explicit expression of the terms to be subtracted. In the cases of D = 3, p = 1 and D = 3, p = 3, we precisely recover the results of parallel plates and three-dimensional box in the literature. Furthermore, for D>p and D = p cases with periodic, Dirichlet and Neumann boundary conditions, we give the explicit expressions of the Casimir free energy in both low temperature (small separations) and high temperature (large separations) regimes, through which the asymptotic behavior of the free energy changing with temperature and the side length is easy to see. We find that for D>p, with the side length going to infinity, the Casimir free energy tends to positive or negative constants or zero, depending on the boundary conditions. But for D = p, the leading term of the Casimir free energy for all three boundary conditions is a logarithmic function of the side length. We also discuss the thermal Casimir force changing with temperature and the side length in different cases and find that when the side length goes to infinity, the force always tends to be zero for different boundary conditions regardless of D>p or D = p. The Casimir free energy and force at high temperature limit behave asymptotically alike that they are proportional to the temperature, be they positive (repulsive) or negative (attractive) in different cases. Our study may be helpful in providing a comprehensive and complete understanding of this old problem.

A twistor model of a free massless spinning particle in four-dimensional Minkowski space is studied in terms of space–time and spinor variables. This model is specified by a simple action, referred to here as the gauged Shirafuji action, that consists of twistor variables and gauge fields on the one-dimensional parameter space. We consider the canonical formalism of the model by following the Dirac formulation for constrained Hamiltonian systems. In the subsequent quantization procedure, we obtain a plane-wave solution with momentum spinors. From this solution and coefficient functions, we construct positive-frequency and negative-frequency spinor wave functions defined on complexified Minkowski space. It is shown that the Fourier–Laplace transforms of the coefficient functions lead to the spinor wave functions expressed as the Penrose transforms of the corresponding holomorphic functions on twistor space. We also consider the exponential generating function for the spinor wave functions and derive a novel representation for each of the spinor wave functions.

The manuscript discovers a new interpretation of counterterms of renormalizable Quantum Field Theories in terms of formal expansions of decorated rooted trees.

An anomaly-free U(1)′ effective Lagrangian as a benchmark of new physics beyond the standard model is proposed to survey the maximal parameter space constrained by the precise electroweak measurements at the Large Electron-Positron Collider (LEP) and direct detection of the dilepton decay channel at at the Large Hadron Collider (LHC). By the global fit of the effective couplings of the Z boson to the Standard Model fermions, parameters Δ₁₁, Δ₂₁ and g^′′Δ₃₁ related to mixings and r related to the U(1)′ charge assignment are bounded. The allowed areas are plotted not only in the r–g^′′ plane, but also in the m_Z′–g^′′ plane. They show that a sub-TeV Z′ is still permissible as long as the coupling g^′′ is of order ~0.01. The results hint at possible new physics beyond the standard model. A prediction of the possible signal for the dilepton decay channel at at LHC is also provided.