We consider semiclassical computation of 3-point correlation functions of (Bogomol’nyi-Prasad-Sommerfeld [BPS] or non-BPS) string states represented by vertex operators carrying large charges in $S^5$. We argue that the ${\mathrm{AdS}}_5$ part of the construction of relevant semiclassical solution involves two basic ingredients: (i) configuration of three glued geodesics in ${\mathrm{AdS}}_2$ suggested by Klose and McLoughlin in [arXiv:1106.0495.] and (ii) a particular Schwarz-Christoffel map of the 3-geodesic solution in cylindrical ($\tau$, $\sigma$) domain into the complex plane with three marked points. This map is constructed using the expression for the ${\mathrm{AdS}}_2$ string stress tensor which is uniquely determined by the 3 scaling dimensions ${\Delta }_i$ as noted by Janik and Wereszczynski in [arXiv:1109.6262] (our solution, however, is different from theirs). We also find the $S^5$ part of the solution and thus the full expression for the semiclassical part of the 3-point correlator for several examples: extremal and nonextremal correlators of BPS states and a particular correlator of “small” circular spinning strings in $S^3\subset S^5$. We demonstrate that for the BPS correlators the results agree with the large charge limit of the corresponding supergravity and free gauge theory expressions.

The mass and interactions of a quantum ’t Hooft-Polyakov monopole are measured nonperturbatively using correlation functions in lattice Monte Carlo simulations. A method of measuring the form factors for interactions between the monopole and fundamental particles, such as the photon, is demonstrated. These quantities are potentially of experimental relevance in searches for magnetic monopoles.

Tensor models and, more generally, group field theories are candidates for higher-dimensional quantum gravity, just as matrix models are in the 2D setting. With the recent advent of a $1/N$ expansion for colored tensor models, more focus has been given to the study of the topological aspects of their Feynman graphs. Crucial to the aforementioned analysis were certain subgraphs known as bubbles and jackets. We demonstrate in the 3D case that these graphs are generated by matrix models embedded inside the tensor theory. Moreover, we show that the jacket graphs represent (Heegaard) splitting surfaces for the triangulation dual to the Feynman graph. With this in hand, we are able to reexpress the Boulatov model as a quantum field theory on these Riemann surfaces.

The perturbative solutions to the semiclassical Einstein field equations describing spherically-symmetric and static lukewarm black hole are constructed. The source term is composed of the (classical) stress-energy tensor of the electromagnetic field and the renormalized stress-energy tensor of the quantized massive scalar field in a large mass limit. We used two different parametrizations. In the first parametrization we calculated the zeroth-order solution. Subsequently, making use of the quantum part of the total stress-energy tensor constructed in the classical background we calculated the corrections to the metric potentials and the corrections to the horizons. This procedure can be thought of as switching the quantized field on and analyzing its influence on the classical background via the back-reaction. In the second parametrization we are looking for a self-consistent lukewarm solution from the very beginning. This requires knowledge of a generic tensor which depend functionally on the metric tensor. The transformation formulas relating the line element in both parametrizations are given.

In this paper, we formulate a generalization of the simple Bekenstein-Sandvik-Barrow-Magueijo theory of varying alpha by allowing the coupling constant $\omega$ for the corresponding scalar field $\psi$ to depend on $\psi$. We focus on the situation where $\omega$ is exponential in $\psi$ and find the late-time behaviors that occur in matter-dominated and dark-energy dominated cosmologies. We also consider the situation when the background expansion scale factor of the Universe evolves in proportion to an arbitrary power of the cosmic time. We find the conditions under which the fine-structure “constant” increases with time, as in the Bekenstein-Sandvik-Barrow-Magueijo theory, and establish a cosmic no-hair behavior for accelerating universes. We also find the conditions under which the fine-structure constant can decrease with time and compare the whole family of models with astronomical data from quasar absorption spectra.

We consider the effect of modified gravity on the peak structure of the cosmic microwave background (CMB) spectrum. We focus on simple models of modified gravity mediated by a massive scalar field coupled to both baryons and cold dark matter. This captures the features of chameleon, symmetron, dilaton, and $f(R)$ models. We find that the CMB peaks can be affected in three independent ways provided the Compton radius of the massive scalar is not far-off the sound horizon at last scattering. When the coupling of the massive scalar to cold dark matter is large, the anomalous growth of the cold dark matter perturbation inside the Compton radius induces a change in the peak amplitudes. When the coupling to baryons is moderately large, the speed of sound is modified and the peaks shifted to higher momenta. Finally when both couplings are nonvanishing, a new contribution proportional to the Newton potential appears in the Sachs-Wolfe temperature and increases the peak amplitudes. We also show how, given any temporal evolution of the scalar field mass, one can engineer a corresponding modified gravity model of the chameleon type. This opens up the possibility of having independent constraints on modified gravity from the CMB peaks and large scale structures at low redshifts.

The problem of time evolution in quantum cosmology is studied in the context of a dust-filled, spatially flat Friedmann-Robertson-Walker universe. In this model, two versions of the commonly-adopted notion of internal time can be implemented in the same quantization, and are found to yield contradictory views of the same quantum state: with one choice, the big-bang singularity appears to be resolved, but with another choice it does not. This and other considerations lead to the conclusion that the notion of internal time as it is usually implemented has no satisfactory physical interpretation. A recently proposed variant of the relational-time construction, using a test clock that is regarded as internal to a specific observer, appears to provide an improved account of time evolution relative to the proper time that elapses along the observer’s worldline. This construction permits the derivation of consistent joint probability densities for observable quantities, which can be viewed either as evolving with proper time or as describing correlations in a timeless manner. It turns out that the observer whose sense of time originates in this test clock will find herself to be living in a bouncing universe.

We examine the three-body baryonic $\overline{B}\to \mathbf{B}{\overline{\mathbf{B}}}^{\prime }V$ decays with $V$ vector mesons in the standard model. We can simultaneously explain the recent experimental data on the decays of $B^{-}\to \Lambda \overline{p}{\rho }^0$ and $\overline{B}\to \Lambda \overline{\Lambda }{\overline{K}}^{*}$ based on the QCD counting rules and $SU(3)$ flavor symmetry. We also predict that the decay branching ratios of ${\overline{B}}^0\to \Lambda \overline{p}{\rho }^{+}$ and $B^{-}\to \Lambda \overline{p}\varphi$ are 3.0 and $1.5\times {10}^{-6}$, respectively, which are promising to be observed by BELLE and BABAR at the $B$ factories.

We apply the double-trace formalism to incorporate nonleptonic weak interactions of mesons into holographic models of the strong interactions. We focus our attention upon $\Delta S=1$ nonleptonic kaon decays. By working with a Yang-Mills–Chern-Simons 5-dimensional action, we explicitly show how, at low energies, one recovers the $\Delta S=1$ weak chiral Lagrangian for both the anomalous and nonanomalous sectors. We provide definite predictions for the low-energy coefficients in terms of the AdS metric and argue that the double-trace formalism is a 5-dimensional avatar of the Weak Deformation Model introduced long ago by Ecker et al. As a significant phenomenological application, we reassess the $K\to 3\pi$ decays in the light of the holographic model. Previous models found a fine-tuned cancellation of resonance exchange in these decays, which was both conceptually puzzling and quantitatively in disagreement with experimental results. The holographic model we build is an illustrative counterexample showing that the cancellation encountered in the literature is not generic but a model-dependent statement and that agreement with experiment can be obtained.

The properties of the thermal Abelian monopoles are studied in the deconfinement phase of the $SU(2)$ gluodynamics. To remove effects of Gribov copies, the simulated annealing algorithm is applied to fix the maximally Abelian gauge. Computing the density of the thermal Abelian monopoles in the temperature range between $1.5T_c$ and $6.9T_c$ we show, by comparison with earlier results, that the Gribov copies effects might be as high as 20%, making proper gauge fixing mandatory. We find that in the infinite temperature limit the monopole density converges to its value in 3-dimensional theory. To study the interaction between monopoles we calculate the monopole-monopole and monopole-antimonopole correlators at different temperatures in the region $(1.5T_c,6.9T_c)$. Using the result of this study we determine the screening mass, monopole-monopole coupling constant, monopole size, and monopole mass. In addition we check the continuum limit of our results.

We study some rare decays of the $B_s$ meson governed by the quark-level transitions $b\to s$, in the fourth generation model popularly known as SM4. Recently, it has been shown that SM4, which is a simple extension of the SM3, can successfully explain several anomalies observed in the $CP$ violation parameters of $B$ and $B_s$ mesons. We find that in this model, due to the additional contributions coming from the heavy $t^{\prime }$ quark in the loop, the branching ratios and other observables in rare $B_s$ decays deviate significantly from their SM values. Some of these modes are within the reach of LHCb experiments, and a search for such channels is strongly argued.

Parity violation in the QCD process is studied using helicity-dependent top-quark pair productions at the Large Hadron Collider experiment. Though no violation can be found in the standard model (SM), new physics beyond the SM predicts the violation in general. In order to evaluate the violation, we utilize an effective operator analysis in a case that new particles predicted by the new physics are too heavy to be directly detected. By using this method, we try to discriminate supersymmetric SM from a universal extra-dimension model via an asymmetry measurement of the top-quark pair production. We also discuss the asymmetry from the SM electroweak top pair production process and that from the little Higgs model.

A complete list of operators contributing at the lowest order to quartic neutral gauge boson couplings involving photons and $Z$-bosons, is presented. We show that, for the couplings we consider, the lowest order contribution is from dimension-eight operators in the case when a light Higgs is present and from dimension-six operators in the Higgsless case where electroweak symmetry is nonlinearly realized. We also show that these operators are generated by exchange of the Kaluza-Klein partners of the graviton in extra-dimensional models. We then explore the possibility of probing these couplings in the diffractive photon fusion processes $pp(\gamma \gamma \to \gamma \gamma )pp$ and $pp(\gamma \gamma \to ZZ)pp$ at the 14 TeV LHC. We find that the $\gamma \gamma \gamma \gamma$ coupling can be probed most sensitively and values as small as $1/(1.8\mathrm{TeV}{)}^4$ can be measured. For the $\gamma \gamma ZZ$ coupling, values as small as $1/(850\mathrm{GeV}{)}^4$ and $1/(1.9\mathrm{TeV}{)}^2$ can be probed in the light Higgs and Higgsless cases, respectively, which is an improvement by orders of magnitude over existing limits.

This paper discusses the two-loop electroweak radiative corrections to the parity-violating $e^{-}{e}^{-}\to e^{-}{e}^{-}(\gamma )(\gamma \gamma )$ scattering asymmetry induced by squaring one-loop diagrams. The calculations are relevant for the ultra-precise 11 GeV MOLLER experiment planned at Jefferson Laboratory and experiments at future high-energy colliders. The imaginary parts of the amplitudes are taken into consideration consistently in both the infrared-finite and divergent terms. The size of the obtained partial correction is significant, which indicates a need for a complete study of the two-loop electroweak radiative corrections in order to meet the precision goals of future experiments.

Enlightened by the idea of the $3\times 3$ Cabibbo-Kobayashi-Maskawa angle matrix proposed recently by Harrison et al., we introduce the Dirac angle matrix $\Phi$ and the Majorana angle matrix $\Psi$ in the lepton sector for Dirac and Majorana neutrinos, respectively. We show that in the presence of $CP$ violation, the angle matrix $\Phi$ or $\Psi$ is entirely equivalent to the complex Maki-Nakagawa-Sakata matrix $V$ itself, but has the advantage of being real, phase rephasing invariant, directly associated to the leptonic unitarity triangles and do not depend on any particular parametrization of $V$. In this paper, we further analyzed how the angle matrices evolve with the energy scale. The one-loop renormalization group equations of $\Phi$, $\Psi$ and some other rephasing invariant parameters are derived and a numerical analysis is performed to compare between the case of Dirac and Majorana neutrinos. Different neutrino mass spectra are taken into account in our calculation. We find that apparently different from the case of Dirac neutrinos, for Majorana neutrinos the renormalization group equation evolutions of $\Phi$, $\Psi$ and $\mathcal{J}$ strongly depend on the Majorana-type $CP$-violating parameters and are more sensitive to the sign of $\Delta m_{31}^2$. They may receive significant radiative corrections in the minimal supersymmetric standard model with large $\tan \beta$ if three neutrino masses are nearly degenerate.

We consider a gravitating spherically symmetric nonrelativistic configuration consisting of a massless chameleon scalar field nonminimally coupled to a perfect isothermal fluid. The object of this paper is to show the influence of the chameleon scalar field on the structure and evolution of an isothermal sphere. For this system we find static, singular and regular solutions depending on the form of the coupling function. A preliminary stability analysis indicates that both stable and unstable solutions exist. For unstable configurations, by choosing the special form of the coupling function, we consider the problem of the gravitational collapse by applying the similarity method.

General relativistic corrections to the galaxy power spectrum appearing at the horizon scale, if neglected, may induce biases on the measured values of the cosmological parameters. In this paper, we study the impact of general relativistic effects on non standard cosmologies such as scenarios with a time dependent dark energy equation of state, with a coupling between the dark energy and the dark matter fluids or with non-Gaussianities. We then explore whether general relativistic corrections affect future constraints on cosmological parameters in the case of a constant dark energy equation of state and of non-Gaussianities. We find that relativistic corrections on the power spectrum are not expected to affect the foreseen errors on the cosmological parameters nor to induce large biases on them.

We study the fluctuations in luminosity distances due to gravitational lensing by large scale ($\gtrsim 35\mathrm{Mpc}$) structures, specifically voids and sheets. We use a simplified “Swiss cheese” model consisting of a $\Lambda \mathrm{CDM}$ Friedman-Robertson-Walker background in which a number of randomly distributed nonoverlapping spherical regions are replaced by mass-compensating comoving voids, each with a uniform density interior and a thin shell of matter on the surface. We compute the distribution of magnitude shifts using a variant of the method of Holz and Wald [2], which includes the effect of lensing shear. The standard deviation of this distribution is $\sim 0.027$ magnitudes and the mean is $\sim 0.003$ magnitudes for voids of radius 35 Mpc, sources at redshift $z_s=1.0$, with the voids chosen so that 90% of the mass is on the shell today. The standard deviation varies from 0.005 to 0.06 magnitudes as we vary the void size, source redshift, and fraction of mass on the shells today. If the shell walls are given a finite thickness of $\sim 1\mathrm{Mpc}$, the standard deviation is reduced to $\sim 0.013$ magnitudes. This standard deviation due to voids is a factor $\sim 3$ smaller than that due to galaxy scale structures. We summarize our results in terms of a fitting formula that is accurate to $\sim 20\%$, and also build a simplified analytic model that reproduces our results to within $\sim 30\%$. Our model also allows us to explore the domain of validity of weak-lensing theory for voids. We find that for 35 Mpc voids, corrections to the dispersion due to lens-lens coupling are of order $\sim 4\%$, and corrections due to shear are $\sim 3\%$. Finally, we estimate the bias due to source-lens clustering in our model to be negligible.

A particular compensation-type solution of the main cosmological constant problem has been proposed recently, with two massless vector fields dynamically canceling an arbitrary cosmological constant $\Lambda$. The naive expectation is that such a compensation mechanism does not allow for the existence of an inflationary phase in the very early Universe. However, it is shown that certain initial boundary conditions on the vector fields can in fact give rise to an inflationary phase.

In this paper, we present a simulation method within the two-component spherical collapse model to investigate dark energy perturbations associated with the formation of dark matter halos. The realistic mass accretion history of a dark matter halo taking into account its fast and slow growth is considered by imposing suitable initial conditions and isotropized virializations for the spherical collapse process. The dark energy component is treated as a perfect fluid described by two important parameters, the equation of state parameter $w$ and the sound speed $c_s$. Quintessence models with $w>-1$ are analyzed. We adopt the Newtonian gauge to describe the spacetime which is perturbed mainly by the formation of a dark matter halo. It is found that the dark energy (DE) density perturbation ${\delta }_{\mathrm{DE}}$ depends on $w$ and $c_s$, and its behavior follows closely the gravitational potential $\Phi$ of the dark matter halo with ${\delta }_{\mathrm{DE}}\approx -(1+w)\Phi /c_s^2$. For $w>-1$, the dark energy perturbation presents a clustering behavior with ${\delta }_{\mathrm{DE}}>0$ during the entire formation of the dark matter halo, from linear to nonlinear and virialized stages. The value of ${\delta }_{\mathrm{DE}}$ increases with the increase of the halo mass. For a cluster of mass $M\sim {10}^{15}{M}_{\odot }$, ${\delta }_{\mathrm{DE}}\sim {10}^{-5}$ within the virialized region for $c_s^2\in [0.5,1]$, and it can reach ${\delta }_{\mathrm{DE}}=O(1)$ with $c_s^2=0.00001$. For a scalar-field dark energy model, we find that with suitably modeled $w$ and $c_s$, its perturbation behavior associated with the nonlinear formation of dark matter halos can well be analyzed using the fluid approach, demonstrating the validity of the fluid description for dark energy even considering its perturbation in the stage of nonlinear dark matter structure formation.