Gauge invariant quark two-point Green’s functions defined with path-ordered gluon field phase factors along skew-polygonal lines joining the quark to the antiquark are considered. Functional relations between Green’s functions with different numbers of path segments are established. An integral equation is obtained for the Green’s function defined with a phase factor along a single straight line. The equation implicates an infinite series of two-point Green’s functions, having an increasing number of path segments; the related kernels involve Wilson loops with contours corresponding to the skew-polygonal lines of the accompanying Green’s function and with functional derivatives along the sides of the contours. The series can be viewed as an expansion in terms of the global number of the functional derivatives of the Wilson loops. The lowest-order kernel, which involves a Wilson loop with two functional derivatives, provides the framework for an approximate resolution of the equation.

We discuss, in the perturbative regime, the scattering of Gaussian pulses of odd-parity gravitational radiation off a nonrotating relativistic star and a Schwarzschild black hole. We focus on the excitation of the $w$-modes of the star as a function of the width $b$ of the pulse and we contrast it with the outcome of a Schwarzschild black hole of the same mass. For sufficiently narrow values of $b$, the waveforms are dominated by characteristic space-time modes. On the other hand, for sufficiently large values of $b$ the backscattered signal is dominated by the tail of the Regge-Wheeler potential, the quasinormal modes are not excited and the nature of the central object cannot be established. We view this work as a useful contribution to the comparison between perturbative results and forthcoming $w$-mode 3D-nonlinear numerical simulation.

Some Riemann-Hilbert (RH) problems are introduced for carrying out symmetry transformations of the 2-dimensional heterotic string theory. A pair of RH transformations are constructed, and they are verified to give an infinite-dimensional symmetry group of the considered theory. This symmetry group has the structure of the semidirect product of the Kac-Moody group $\widehat{O(d,d+n)}$ and Virasoro group. Moreover, the infinitesimal forms of these RH transformations are calculated out, and they are found to give exactly the same results as in my previous paper. These demonstrate that the pair of RH transformations in the current paper provide exponentiations of all the infinitesimal symmetries in my previous paper. The finite forms of symmetry transformations given in the present paper are more important and useful for theoretic studies and new solution generation, etc.

We construct a new charged rotating Kaluza-Klein black hole solution in the five-dimensional Einstein-Maxwell theory with a Chern-Simon term. The features of the solutions are also investigated. The spacetime is asymptotically locally flat, i.e., it asymptotes to a twisted $S^1$ bundle over the four-dimensional Minkowski spacetime. The solution describe a non-BPS black hole rotating in the direction of the extra dimension. The solutions have the limits to the supersymmetric black hole solutions, a new extreme non-BPS black hole solution and a new rotating non-BPS black hole solution with a constant twisted $S^1$ fiber.

The negative mode of the Schwarzschild black hole is central to Euclidean quantum gravity around hot flat space and for the Gregory-Laflamme black-string instability. Numerous gauges were employed in the past to analyze it. Here the analytic derivation is found, based on postponing the gauge-fixing, on the power of the action and on decoupling of nondynamic fields. A broad-range generalization to perturbations around geometries with one nonhomogeneous dimension is discussed.

In general relativity, the gyromagnetic ratio for all stationary, axisymmetric, and asymptotically flat Einstein-Maxwell fields is known to be $g=2$. In this paper, we continue our previous works of examination of this result for rotating charged spacetimes with asymptotic nonflat structure. We first consider two instructive examples of these spacetimes: The spacetime of a Kerr-Newman black hole with a straight cosmic string on its axis of symmetry and the Kerr-Newman Taub-NUT (Newman-Unti-Tamburino) spacetime. We show that for both spacetimes the gyromagnetic ratio $g=2$ independent of their asymptotic structure. We also extend this result to a general class of metrics which admit separation of variables for the Hamilton-Jacobi and wave equations. We proceed with the study of the gyromagnetic ratio in higher dimensions by considering the general solution for rotating charged black holes in minimal five-dimensional gauged supergravity. We obtain the analytic expressions for two distinct gyromagnetic ratios of these black holes that are associated with their two independent rotation parameters. These expressions reveal the dependence of the gyromagnetic ratio on both the curvature radius of the AdS background and the parameters of the black holes: The mass, electric charge, and two rotation parameters. We explore some special cases of interest and show that when the two rotation parameters are equal to each other and the rotation occurs at the maximum angular velocity, the gyromagnetic ratio $g=4$ regardless of the value of the electric charge. This agrees precisely with our earlier result obtained for general Kerr-AdS black holes with a test electric charge. We also show that in the Bogomol’nyi-Prasad-Sommerfield (BPS) limit the gyromagnetic ratio for a supersymmetric black hole with equal rotation parameters ranges between 2 and 4.

The baryonic acoustic signature in the large-scale clustering pattern of galaxies has been detected in the two-point correlation function. Its precise spatial scale has been forwarded as a rigid-rod ruler test for the space-time geometry, and hence as a probe for tracking the evolution of dark energy. Percent-level shifts in the measured position can bias such a test and erode its power to constrain cosmology. This paper addresses some of the systematic effects that might induce shifts; namely, nonlinear corrections from matter evolution, redshift space distortions, and biasing. We tackle these questions through analytic methods and through a large battery of numerical simulations, with total volume of the order $\sim 100[{\mathrm{Gpc}}^3{h}^{-3}]$. A toy-model calculation shows that if the nonlinear corrections simply smooth the acoustic peak, then this gives rise to an “apparent” shifting to smaller scales. However if tilts in the broadband power spectrum are induced then this gives rise to more pernicious “physical” shifts. Our numerical simulations show evidence of both: in real space and at $z=0$, for the dark matter we find percent-level shifts; for haloes the shifts depend on halo mass, with larger shifts being found for the most biased samples, up to 3%. From our analysis we find that physical shifts are greater than $\sim 0.4\%$ at $z=0$ for a LCDM model with ${\sigma }_8=0.9$. In redshift space these effects are exacerbated, but at higher redshifts are alleviated. We develop an analytical model to understand this, based on solutions to the pair conservation equation using characteristic curves. When combined with modeling of pairwise velocities the model reproduces the main trends found in the data. The model may also help to unbias the acoustic peak.

We construct a class of scalar field models coupled to matter that lead to the dependence of masses and coupling constants on the ambient matter density. Such models predict a deviation of couplings measured on the Earth from values determined in low-density astrophysical environments, but do not necessarily require the evolution of coupling constants with the redshift in the recent cosmological past. Additional laboratory and astrophysical tests of $\Delta \alpha$ and $\Delta (m_p/m_e)$ as functions of the ambient matter density are warranted.

While vector modes are usually ignored in cosmology since they are not produced during inflation they are inevitably produced from the interaction of density fluctuations of differing wavelengths. This effect may be calculated via a second-order perturbative expansion. We investigate this effect during the radiation era. We discuss the generation mechanism by investigating two scalar modes interacting, and we calculate the power of vector modes generated by a power-law spectrum of density perturbations on all scales.

Quantum gravity effects are expected to modify the primordial density fluctuations produced during inflation and leave their imprint on the cosmic microwave background observed today. We present a new analysis discussing whether these effects are detectable, considering both currently available data and simulated results from an optimal CMB experiment. We find that the WMAP (Wilkinson Microwave Anisotropy Probe) data show no evidence for the particular signature considered in this work but give an upper bound on the parameters of the model. However, a hypothetical experiment shows that with proper data, the trans-Planckian effects should be detectable through alternate sampling methods. This fuzzy conclusion is a result of the nature of the oscillations, since they give rise to a likelihood hypersurface riddled with local maxima. A simple Bayesian analysis shows no significant evidence for the simulated data to prefer a trans-Planckian model. Conventional Markov chain Monte Carlo (MCMC) methods are not suitable for exploring this complicated landscape, but alternative methods are required to solve the problem. This, however, requires extremely high-precision data.

We study the dynamics of the closed scalar field FRW cosmological models in the framework of the so-called unified dark matter (UDM) scenario. Performing a theoretical as well as a numerical analysis we find that there is a strong indication of chaos in agreement with previous studies. We find that a positive value of the spatial curvature is essential for the appearance of chaoticity, though the Lyapunov number seems to be independent of the curvature value. Models that are close to flat ($k\to 0^{+}$) exhibit a chaotic behavior after a long time while pure flat models do not exhibit any chaos. Moreover, we find that some of the semiflat models in the UDM scenario exhibit similar dynamical behavior with the $\Lambda$ cosmology despite their chaoticity. Finally, we compare the measured evolution of the Hubble parameter derived from the differential ages of passively evolving galaxies with that expected in the semiflat unified scalar field cosmology. Based on a specific set of initial conditions we find that the UDM scalar field model matches well the observational data.

Superstring theory predicts the potential formation of string networks with bound states ending in junctions. Kinematic constraints for junction formation have been derived within the Nambu-Goto thin string approximation. Here we test these constraints numerically in the framework of the Abelian-Higgs model in the Type-I regime and report on good agreement with the analytical predictions. We also demonstrate that strings can effectively pass through each other when they meet at speeds slightly above the critical velocity permitting bound-state formation. This is due to reconnection effects that are beyond the scope of the Nambu-Goto approximation.

By finding the spinor eigenvalues for a single deficit angle $(d-2)$-sphere, we derive the radial potential for fermions on a $d$-dimensional black hole background that is embedded on a codimension-two brane with conical singularity, where the deficit angle is related to the brane tension. From this we obtain the quasinormal mode spectrum for bulk fermions on such a background. As a by-product of our method, this also gives a rigorous proof for integer spin fields on the deficit 2-sphere.

We propose using the lightest $CP$-even Higgs boson in the minimal supersymmetric standard model to probe the stop sector. Unlike measuring stop masses in production/decay processes which requires knowledge of masses and mixing angles of other superparticles, our strategy depends little on supersymmetric parameters other than those in the stop sector in a large region of the parameter space. We show that measurements of the Higgs mass and the production rate in the gluon fusion channel, the dominant channel at the CERN LHC, allow for determination of two parameters in the stop mass-squared matrix, including the off-diagonal mixing term. This proposal is very effective when stops are light and their mixing is large, which coincides with the region where the electroweak symmetry breaking is minimally fine-tuned. We also argue that a lightest $CP$-even Higgs mass in the upper range of allowed values and a production rate significantly smaller than the rate predicted in the standard model would be difficult to reconcile within the minimal supersymmetric standard model, except in extreme corners of the parameter space.

We consider a gauge extension of the electroweak sector of the standard model based on the group ${\mathrm{G}}_2\times \mathrm{SU}(2)\times \mathrm{U}(1)$. The exceptional group ${\mathrm{G}}_2$ is the smallest rank two group that contains SU(3) as a subgroup; the SU(3) prediction ${sin}^2{\theta }_w=1/4$ follows approximately in this model if the couplings of the additional SU(2) and U(1) factors are sufficiently large. We study the symmetry-breaking sector of the model, the bounds from precision electroweak constraints and the mass spectrum of exotic gauge bosons that may be produced at future colliders. We also discuss a SU(3) electroweak model in which a vectorlike sector is included explicitly to facilitate the decays of otherwise stable exotic states. The models considered here represent plausible extensions of the minimal SU(3) electroweak model with potentially distinctive TeV-scale phenomenology.

We study the Möller and Bhabha scattering in the noncommutative extension of the standard model using the Seiberg-Witten maps of this to first order of the noncommutative parameter ${\theta }_{\mu \nu }$. We look at the angular distribution $d\sigma /d\Omega$ to explore the noncommutativity of space-time at around ${\Lambda }_{\mathrm{NC}}\sim \mathrm{TeV}$ and find that the distribution deviates significantly from the one obtained from the commutative version of the standard model.

We revisit the implications of the $R$-invariant new inflation model to the supersymmetric standard model in light of recent discussion of gravitino production processes by the decay of the inflaton and the supersymmetry breaking field. We show that the models with supergravity mediation do not work well together with the $R$-invariant new inflation model, where the gravitino abundance produced by the decay of the inflaton and the supersymmetry breaking field significantly exceeds the bounds from cosmological observations without fine-tuning. We also show that the models with gauge mediation can go together with the $R$-invariant new inflation model, where the dark matter abundance and the baryon asymmetry of the universe are consistently explained without severe fine-tuning.

An extension of the gauge group $SU(2{)}_L\otimes U(1{)}_Y$ of the standard model to the symmetry group $SU(4{)}_L\otimes U(1{)}_X$ (3-4-1 for short) is presented. The model does not contain exotic electric charges and anomaly cancellation is achieved with a family of quarks transforming differently from the other two, thus leading to FCNC. By introducing a discrete $Z_2$ symmetry we obtain a consistent fermion mass spectrum, and avoid unitarity violation of the Cabibbo-Kobayashi-Maskawa mixing matrix arising from the mixing of ordinary and exotic quarks. The neutral currents coupled to all neutral vector bosons are studied, and by using CERN LEP and SLAC Linear Collider data at $Z$-pole and atomic parity violation data, we bound parameters of the model related to tree-level $Z-Z^{\prime }$ mixing. These parameters are further constrained by using experimental input from neutral meson mixing in the analysis of sources of FCNC present in the model. Constraints coming from the contribution of exotic particles to the one-loop oblique electroweak parameters $S$, $T$ and $U$ are also briefly discussed. Finally, a comparison is done of the predictions of different classes of 3-4-1 models without exotic electric charges.

We study the role of diquarks in light baryons through point-to-point baryon correlators. We contrast results from quenched simulations with ones with two flavors of dynamical overlap fermions. The scalar, pseudoscalar, and axial vector diquarks are combined with light quarks to form color singlets. The quenched simulation shows large zero-mode effects in correlators containing the scalar and pseudoscalar diquark. The two scalar diquarks created by ${\gamma }_5$ and ${\gamma }_0{\gamma }_5$ lead to different behavior in baryon correlators, showing that the interaction of diquarks with the third light quark matters: we do not see an isolated diquark. In our quark mass range, the scalar diquark created by ${\gamma }_5$ seems to play a greater role than the others.

The available data on neutron scattering were reviewed to constrain a hypothetical new short-range interaction. We show that these constraints are several orders of magnitude better than those usually cited in the range between 1 pm and 5 nm. This distance range occupies an intermediate space between collider searches for strongly coupled heavy bosons and searches for new weak macroscopic forces. We emphasize the reliability of the neutron constraints insofar as they provide several independent strategies. We have identified a promising way to improve them.