The anomalous scaling behavior of the topological susceptibility ${\chi }_t$ in two-dimensional $C{P}^{N-1}$ sigma models for $N\le 3$ is studied using the overlap Dirac operator construction of the lattice topological charge density. The divergence of ${\chi }_t$ in these models is traced to the presence of small instantons with a radius of order $a(=\mathrm{\text{lattice spacing}})$, which are directly observed on the lattice. The observation of these small instantons provides detailed confirmation of Lüscher’s argument that such short-distance excitations, with quantized topological charge, should be the dominant topological fluctuations in $C{P}^1$ and $C{P}^2$, leading to a divergent topological susceptibility in the continuum limit. For the $C{P}^{N-1}$ models with $N>3$ the topological susceptibility is observed to scale properly with the mass gap. These larger $N$ models are not dominated by instantons, but rather by coherent, one-dimensional regions of topological charge which can be interpreted as domain wall or Wilson line excitations and are analogous to D-brane or “Wilson bag” excitations in QCD. In Lorentz gauge, the small instantons and Wilson line excitations can be described, respectively, in terms of poles and cuts of an analytic gauge potential.

We study the baryonic sector of QCD with quarks in the two-index symmetric or antisymmetric representation. The minimal gauge invariant state that carries baryon number cannot be identified with the Skyrmion of the low-energy chiral effective Lagrangian. Mass, statistics, and baryon number do not match. We carefully investigate the properties of the minimal baryon in the large $N$ limit and we find that it is unstable under formation of bound states with higher baryonic number. These states match exactly with the properties of the Skyrmion of the effective Lagrangian.

This paper extends the calculation of quantum corrections to the cosmological correlation $⟨\zeta \zeta ⟩$, which has been done by Weinberg for a loop of minimally coupled scalars, to other types of matter loops and a general and realistic potential. It is shown here that departures from scale invariance are never large even when Dirac, vector, and conformal scalar fields are present during inflation. No fine-tuning is needed, in the sense that effective masses or coupling constants can have arbitrary values. Even when the mass is as large as $M_{\mathrm{Pl}}$, the one-loop result is still naturally smaller than the classical one. Thus, the results show that the existence of these fields during inflation may not be ruled out and is consistent with natural reheating.

Presented in this paper is the description of a Markov chain Monte Carlo (MCMC) routine for conducting coherent parameter estimation for interferometric gravitational wave observations of an inspiral of binary compact objects using multiple detectors. Data from several interferometers are processed, and all nine parameters (ignoring spin) associated with the binary system are inferred, including the distance to the source, the masses, and the location on the sky. The data is matched with time-domain inspiral templates that are 2.5 post-Newtonian (PN) in phase and 2.0 PN in amplitude. We designed and tuned an MCMC sampler so that it is able to efficiently find the posterior mode(s) in the parameter space and perform the stochastic integration necessary for inference within a Bayesian framework. Our routine could be implemented as part of an inspiral detection pipeline for a world-wide network of detectors. Examples are given for simulated signals and data as seen by the LIGO and Virgo detectors operating at their design sensitivity.

We study the dynamics of colliding domain walls including self-gravity. The initial data is set up by applying a Bogomol’nyi-Prasad-Sommerfield (BPS) domain wall in five-dimensional supergravity, and we evolve the system determining the final outcome of collisions. After a collision, a spacelike curvature singularity covered by a horizon is formed in the bulk, resulting in a black brane with trapped domain walls. This is a generic consequence of collisions, except for nonrelativistic weak field cases, in which the walls pass through one another or multiple bounces take place without singularity formation. These results show that incorporating the self-gravity drastically changes a naive picture of colliding branes.

We present the application of a novel method of time-series analysis, the Hilbert-Huang transform, to the search for gravitational waves. This algorithm is adaptive and does not impose a basis set on the data, and thus the time-frequency decomposition it provides is not limited by time-frequency uncertainty spreading. Because of its high time-frequency resolution it has important applications to both signal detection and instrumental characterization. Applications to the data analysis of the ground and space based gravitational wave detectors, LIGO and LISA, are described.

One of the most straightforward ways to address the flavor problem of low-energy supersymmetry is to arrange for the scalar soft terms to vanish simultaneously at a scale $M_c$ much larger than the electroweak scale. This occurs naturally in a number of scenarios, such as no-scale models, gaugino mediation, and several models with strong conformal dynamics. Unfortunately, the most basic version of this approach that incorporates gaugino mass unification and zero scalar masses at the grand unification scale is not compatible with collider and dark matter constraints. However, experimental constraints can be satisfied if we exempt the Higgs bosons from flowing to zero mass value at the high scale. We survey the theoretical constructions that allow this and investigate the collider and dark matter consequences. A generic feature is that the sleptons are relatively light. Because of this, these models frequently give a significant contribution to the anomalous magnetic moment of the muon, and neutralino-slepton coannihilation can play an important role in obtaining an acceptable dark matter relic density. Furthermore, the light sleptons give rise to a large multiplicity of lepton events at colliders, including a potentially suggestive clean trilepton signal at the Tevatron, and a substantial four lepton signature at the LHC.

We calculate the branching ratios and $CP$-violating asymmetries for $B^0\to \omega \eta ,\omega {\eta }^{\prime },\varphi \eta$, and $\varphi {\eta }^{\prime }$ decays in the perturbative QCD (pQCD) factorization approach. The pQCD predictions for the $CP$-averaged branching ratios are $\mathrm{Br}(B^0\to \omega \eta )=({2.7}_{-1.0}^{+1.1})\times {10}^{-7}$, $\mathrm{Br}(B^0\to \omega {\eta }^{\prime })=({0.75}_{-0.33}^{+0.37})\times {10}^{-7}$, and $\mathrm{Br}(B^0\to \varphi \eta )=({6.3}_{-1.9}^{+3.3})\times {10}^{-9}$, $\mathrm{Br}(B^0\to \varphi {\eta }^{\prime })=({7.3}_{-2.6}^{+3.5})\times {10}^{-9}$ which are consistent with currently available experimental upper limits. The inclusion of the gluonic contribution can change the branching ratios of $B\to \omega (\varphi ){\eta }^{\prime }$ decays by about 10%. The direct $CP$-violating asymmetries for $B^0\to \omega \eta$ and $\omega {\eta }^{\prime }$ decays are generally large in size.

A global analysis of the experimental data on azimuthal asymmetries in semi-inclusive deep inelastic scattering (SIDIS), from the HERMES and COMPASS Collaborations, and in $e^{+}{e}^{-}\to h_1{h}_{2}X$ processes, from the Belle Collaboration, is performed. It results in the extraction of the Collins fragmentation function and, for the first time, of the transversity distribution function for $u$ and $d$ quarks. These turn out to have opposite signs and to be sizably smaller than their positivity bounds. Predictions for the azimuthal asymmetry $A_{UT}^{\sin ({\varphi }_S+{\varphi }_h)}$, as will soon be measured at JLab and COMPASS operating on a transversely polarized proton target, are then presented.

A search of axions produced in nuclear transitions was performed at the Kuo-Sheng Nuclear Power Station with a high-purity germanium detector of mass 1.06 kg at a distance of 28 m from the 2.9 GW reactor core. The expected experimental signatures were monoenergetic lines produced by their Primakoff or Compton conversions at the detector. Based on $459.0/96.3$ days of reactor ON/OFF data, no evidence of axion emissions were observed and constraints on the couplings $g_{a\gamma \gamma }$ and $g_{aee}$ versus axion mass $m_a$ within the framework of invisible axion models were placed. The KSVZ and DFSZ models can be excluded for ${10}^4\mathrm{eV}\lesssim m_a\lesssim {10}^6\mathrm{eV}$. Model-independent constraints on $g_{a\gamma \gamma }·g_{aNN}^1<7.7\times {10}^{-9}{\mathrm{GeV}}^{-2}$ for $m_a\lesssim {10}^5\mathrm{eV}$ and $g_{aee}·g_{aNN}^1<1.3\times {10}^{-10}$ for $m_a\lesssim {10}^6\mathrm{eV}$ at 90% confidence level were derived. This experimental approach provides a unique probe for axion mass at the keV-MeV range not accessible to the other techniques.

We discuss the possibility of obtaining the present acceleration of the Universe via $f(R)$ gravity theories which recently attracted much attention. It is known that $f(R)$ theories generally have room for this. In this work we stress that the requirement for the stabilization of extra dimensions is naturally incorporated in such a generalization of Einstein gravity under rather orthodox assumptions. We have restricted our study to pure $f(R)$ gravity without additional matter sources partially in view of the fact that if the acceleration is to continue indefinitely any ordinary matter term is to redshift to irrelevancy and mostly for economy in understanding. The general conditions we find are that the manifold of the extra dimensional space is to have negative internal curvature and that the Ricci scalar of the full space-time manifold is also negative. The positive curvature case for an extra dimensional manifold is actually the most generic case. However, this necessitates a fine-tuning between the Hubble constant and the size of extra dimensions in the absence of matter sources.

We study the production of loops in the cosmic string network in the expanding background by means of a numerical simulation exact in the flat-spacetime limit and first order in the expansion rate. We find an initial regime characterized by production of small loops at the scale of the initial correlation length, but later we see the emergence of a scaling regime of loop production. This qualitatively agrees with earlier expectations derived from the results of flat-spacetime simulations. In the final scaling regime we find that the characteristic length of loops scales as $\sim 0.1t$ in both radiation and matter eras.

The situation that a scalar field provides the source of the accelerated expansion of the Universe while rolling down its potential is common in both the simple models of the primordial inflation and the quintessence-based dark energy models. Motivated by this point, we address the possibility of causing the current acceleration via the primordial inflation using a simple model based on hybrid inflation. We trigger the onset of the motion of the quintessence field via the waterfall field, and find that the fate of the Universe depends on the true vacuum energy determined by choosing the parameters. We also briefly discuss the variation of the equation of state and the possible implementation of our scenario in supersymmetric theories.

We point out that the correlation between the large atmospheric neutrino mixing and the $b\to s$ transition, if it exists, comes from the lopsided flavor structure in SO(10) grand unification theory. We suggest testing the correlation by studying the deviation of $S_{\varphi K_S}$ and $S_{{\eta }^{\prime }{K}_S}$ from the standard model predictions along with the constraints from $\Delta M_{B_S}$ and $b\to s\gamma$ in a realistic SO(10) model with lopsided flavor structure. We find a specific correlation between $S_{\varphi K_S}$ and $S_{{\eta }^{\prime }{K}_S}$ that is intrinsic to the lopsided structure and discuss how to confirm or rule out this flavor pattern by the more accurate measurements of these $CP$ violation quantities in $B$ decay.

In a previous work we showed that, in a suitable setting, one can use diffeomorphism invariance in order to derive gravitational field equations from boundary terms of the gravitational action. Standing by our results we reply here to a recent comment questioning their validity.

It has recently been suggested that the gravitational dynamics could be obtained by requiring the action to be invariant under diffeomorphism transformations. We argue that the action constructed in a usual way is automatically diffeomorphism invariant in nature, which thus invalidates this alternative perspective to obtain gravitational dynamics. Especially, we also show what is wrong with the technical derivation of gravitational dynamics in the alternative approach.

The rate of the nonperturbative decay of a ’t Hooft-Polyakov monopole into a dyon and a charged fermion is calculated in an external electric field. The subleading semiclassical preexponential factor is presented. The leading exponential factor is shown to be in full agreement with the previous results derived in a different technique. Analogous treatment is shown to hold for the two-fermionic decay of the lightest bound state in Thirring model. Thus restoring the “effective meson-fermion vertex” becomes possible.

As a continuation of the work by Minamitsuji, Naylor, and Sasaki [J. High Energy Phys. 12 (2006) 079], we discuss the Casimir effect for a massless bulk scalar field in a 4D toy model of a 6D warped flux compactification model, to stabilize the volume modulus. The one-loop effective potential for the volume modulus has a form similar to the Coleman-Weinberg potential. The stability of the volume modulus against quantum corrections is related to an appropriate heat kernel coefficient. However, to make any physical predictions after volume stabilization, knowledge of the derivative of the zeta function, ${\zeta }^{\prime }(0)$ (in a conformally related spacetime) is also required. By adding up the exact mass spectrum using zeta-function regularization, we present a revised analysis of the effective potential. Finally, we discuss some physical implications, especially concerning the degree of the hierarchy between the fundamental energy scales on the branes. For a larger degree of warping our new results are very similar to the ones given by Minamitsuji, Naylor, and Sasaki [J. High Energy Phys. 12 (2006) 079] and imply a larger hierarchy. In the nonwarped (rugby ball) limit the ratio tends to converge to the same value, independently of the bulk dilaton coupling.

We present perturbative calculations made with domain-wall fermions which possess a finite number of points $N_s$ in the extra fifth dimension. We have derived the required propagator functions, investigated the one-loop properties of quark amplitudes at finite $N_s$, and evaluated three quantities that can provide insights on chirality-breaking effects from the perturbative side. First we have computed the residual mass for various choices of $N_s$ and of the domain-wall height $M$. We have found that this radiatively induced mass approaches zero reasonably fast with the extent of the fifth dimension, depending on $M$ and on a lesser extent on the coupling $g_0$. We have also computed the differences of the renormalization constants of the vector and axial-vector currents and of the scalar and pseudoscalar densities. Finally we have calculated the chirally forbidden mixing (which at finite $N_s$ is suppressed only partially) of an operator which describes the lowest moment of the $g_2$ structure function. The quantities that we have studied turn out to lose gauge invariance when $N_s$ is not infinite. We have also found that anomalous dimensions of operators at finite $N_s$ generally depend on $N_s$ and $M$. In particular, the vector and axial-vector currents have in general a nonzero anomalous dimension at finite $N_s$.