An $S$ matrix satisfying the Yang-Baxter equation with symmetries relevant to the ${\mathrm{AdS}}_5\times S^5$ superstring recently has been determined up to an unknown scalar factor. Such scalar factors are typically fixed using crossing relations; however, due to the lack of conventional relativistic invariance, in this case its determination remained an open problem. In this paper we propose an algebraic way to implement crossing relations for the ${\mathrm{AdS}}_5\times S^5$ superstring worldsheet $S$ matrix. We base our construction on a Hopf-algebraic formulation of crossing in terms of the antipode and introduce generalized rapidities living on the universal cover of the parameter space which is constructed through an auxillary, coupling-constant dependent, elliptic curve. We determine the crossing transformation and write functional equations for the scalar factor of the $S$ matrix in the generalized rapidity plane.

We study the motion of higher dimensional fermions in a nonsingular 6D brane background with an increasing warp factor. This background acts as a potential well trapping fermions and fields of other spins near a $3+1$ dimensional brane. By adjusting the shape of this potential well it is possible to obtain three normalizable zero-mass modes giving a possible higher dimensional solution to the fermion generation puzzle. The three different zero-mass modes correspond to the different angular momentum eigenvalues for rotations around the brane. This bulk angular momentum acts as the family or generation number. The three normalizable zero modes have different profiles with respect to the bulk, thus by coupling the higher dimensional fermion field to a higher dimensional scalar field it is possible to generate both a realistic mass hierarchy and realistic mixings between the different families.

Inflationary consistency equations relate the scalar and tensor perturbations. We elucidate the infinite hierarchy of consistency equations of single-field inflation, the first of which is the well-known relation $A_{\mathrm{T}}^2/A_{\mathrm{S}}^2=-n_{\mathrm{T}}/2$ between the amplitudes and the tensor spectral index. We write a general expression for all consistency equations both to first and second order in the slow-roll expansion. We discuss the relation to other consistency equations that have appeared in the literature, demonstrating in particular that the approximate consistency equation recently introduced by Chung and collaborators is equivalent to the second consistency equation of Lidsey et al. (1997).

We investigate non-Gaussianity in general multiple-field inflation using the formalism we developed in earlier papers. We use a perturbative expansion of the nonlinear equations to calculate the three-point correlator of the curvature perturbation analytically. We derive a general expression that involves only a time integral over background and linear perturbation quantities. We work out this expression explicitly for the two-field slow-roll case, and find that non-Gaussianity can be orders of magnitude larger than in the single-field case. In particular, the bispectrum divided by the square of the power spectrum can easily be of $\mathcal{O}(1–10)$, depending on the model. Our result also shows the explicit momentum dependence of the bispectrum. This conclusion of large non-Gaussianity is confirmed in a semianalytic investigation of a simple quadratic two-field model.

We develop a nonlinear framework for describing long-wavelength perturbations in multiple-field inflation. The basic variables describing inhomogeneities are defined in a nonperturbative manner, are invariant under changes of time slicing on large scales and include both matter and metric perturbations. They are combinations of spatial gradients generalizing the gauge-invariant variables of linear theory. Dynamical equations are derived and supplemented with stochastic source terms which provide the long-wavelength initial conditions determined from short-wavelength modes. Solutions can be readily obtained via numerical simulations or analytic perturbative expansions. The latter are much simpler than the usual second-order perturbation theory. Applications are given in a companion paper.

High-$z$ galaxy redshift surveys open up exciting possibilities for precision determinations of neutrino masses and inflationary models. The high-$z$ surveys are more useful for cosmology than low-$z$ ones owing to much weaker nonlinearities in matter clustering, redshift-space distortion, and galaxy bias, which allows us to use the galaxy power spectrum down to the smaller spatial scales that are inaccessible by low-$z$ surveys. We can then utilize the two-dimensional information of the linear power spectrum in angular and redshift space to measure the scale-dependent suppression of matter clustering due to neutrino free-streaming as well as the shape of the primordial power spectrum. To illustrate capabilities of high-$z$ surveys for constraining neutrino masses and the primordial power spectrum, we compare three future redshift surveys covering 300 square degrees at $0.5<z<2$, $2<z<4$, and $3.5<z<6.5$. We find that, combined with the cosmic microwave background data expected from the Planck satellite, these surveys allow precision determination of the total neutrino mass with the projected errors of $\sigma (m_{\nu ,\mathrm{tot}})=0.059$, 0.043, and 0.025 eV, respectively, thus yielding a positive detection of the neutrino mass rather than an upper limit, as $\sigma (m_{\nu ,\mathrm{tot}})$ is smaller than the lower limits to the neutrino masses implied from the neutrino oscillation experiments, by up to a factor of 4 for the highest redshift survey. The accuracies of constraining the tilt and running index of the primordial power spectrum, $\sigma (n_s)=(3.8,3.7,3.0)\times {10}^{-3}$ and $\sigma ({\alpha }_s)=(5.9,5.7,2.4)\times {10}^{-3}$ at $k_0=0.05{\mathrm{Mpc}}^{-1}$, respectively, are smaller than the current uncertainties by more than an order of magnitude, which will allow us to discriminate between candidate inflationary models. In particular, the error on ${\alpha }_s$ from the future highest redshift survey is not very far away from the prediction of a class of simple inflationary models driven by a massive scalar field with self-coupling, ${\alpha }_s=-(0.8–1.2)\times {10}^{-3}$.

In this paper we discuss a new method which can be used to obtain arbitrarily accurate analytical expressions for the deflection angle of light propagating in a given metric. Our method works by mapping the integral into a rapidly convergent series and provides extremely accurate approximations already to first order. We have derived a general first order formula for a generic spherically symmetric static metric tensor and we have tested it in four different cases.

In this paper we study the double diffractive vector meson production in $e^{+}{e}^{-}$ collisions assuming the dominance of the BFKL pomeron exchange. We consider the nonforward solution of the BFKL equation at high energy and large momentum transfer and estimate the total cross section for the process $e^{+}{e}^{-}\to e^{+}{e}^{-}{V}_1{V}_2$ with antitagged $e^{+}$ and $e^{-}$, where $V_1$ and $V_2$ can be any two vector mesons ($V_i=\rho ,\omega ,\varphi ,J/\Psi ,{\rm Y}$). The event rates for the future linear colliders are given.

Recent phenomenological work has examined two different ways of including charge symmetry violation in parton distribution functions. First, a global phenomenological fit to high energy data has included charge symmetry breaking terms, leading to limits on the magnitude of parton charge symmetry breaking. In a second approach, two groups have included the coupling of partons to photons in the QCD evolution equations. One possible experiment that could search for isospin violation in parton distributions is a measurement of the asymmetry in $W$ production at a collider. In this work we include both of the postulated sources of parton charge symmetry violation. We show that, given charge symmetry violation of a magnitude consistent with existing high energy data, the expected $W$ production asymmetries would be quite small, generally less than 1%.

We study the quantum mechanical correlation between two identical neutralinos in the decays of minimal supersymmetric standard model (MSSM) scalar tau (stau) pair produced in $e^{+}{e}^{-}$ annihilation. Generally, the decay products of scalar (spinless) particles are not correlated. We show that a correlation between two neutralinos appears near pair production threshold, due to a finite stau width and mixing of the staus and/or neutralinos, and because the neutralinos are Majorana. Because the correlation is significant only in a specific kinematical configuration, it can be observed only in supersymmetric models where the neutralino momenta can be kinematically reconstructed, such as in models with $R$-parity violation.

We present a fit to measured moments of inclusive distributions in $B\to X_c\ell \overline{\nu }$ and $B\to X_s\gamma$ decays to extract values for the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{cb}|$, the $b$- and $c$-quark masses, and higher-order parameters that appear in the heavy quark expansion. The fit is carried out using theoretical calculations in the kinetic scheme and includes moment measurements of the BABAR, Belle, CDF, CLEO, and DELPHI collaborations for which correlation matrices have been published. We find $|V_{cb}|=(41.96\pm {0.23}_{\exp }\pm {0.35}_{\mathrm{HQE}}\pm {0.59}_{{\Gamma }_{\mathrm{SL}}})\times {10}^{-3}$ and $m_b=4.590\pm {0.025}_{\exp }\pm {0.030}_{\mathrm{HQE}}\mathrm{GeV}$ where the errors are experimental and theoretical respectively. We also derive values for the heavy quark distribution function parameters $m_b$ and ${\mu }_{\pi }^2$ in different theoretical schemes that can be used as input for the determination of $|V_{ub}|$.

A relativistic positioning system is a physical realization of a coordinate system consisting in four clocks in arbitrary motion broadcasting their proper times. The basic elements of the relativistic positioning systems are presented in the two-dimensional case. This simplified approach allows to explain and to analyze the properties and interest of these new systems. The positioning system defined by geodesic emitters in flat metric is developed in detail. The information that the data generated by a relativistic positioning system give on the space-time metric interval is analyzed, and the interest of these results in gravimetry is pointed out.

Recently, there have been suggestions that the apparent accelerated expansion of the universe is not caused by repulsive gravitation due to dark energy, but is rather a result of inhomogeneities in the distribution of matter. In this work, we investigate the behavior of a dust-dominated inhomogeneous Lemaître-Tolman-Bondi universe model, and confront it with various astrophysical observations. We find that such a model can easily explain the observed luminosity distance-redshift relation of supernovae without the need for dark energy, when the inhomogeneity is in the form of an underdense bubble centered near the observer. With the additional assumption that the universe outside the bubble is approximately described by a homogeneous Einstein-de Sitter model, we find that the position of the first peak in the cosmic microwave background (CMB) power spectrum can be made to match the WMAP observations. Whether or not it is possible to reproduce the entire CMB angular power spectrum in an inhomogeneous model without dark energy is still an open question.

We consider a large class of models where the $SU(5)$ gauge symmetry and a Froggatt-Nielsen (FN) Abelian flavor symmetry arise from a $U(5)\times U(5)$ quiver gauge theory. An intriguing feature of these models is a relation between the gauge representation and the horizontal charge, leading to a restricted set of possible FN charges. Requiring that quark masses are hierarchical, the lepton flavor structure is uniquely determined. In particular, neutrino mass anarchy is predicted.

We point out a set of operator identities that relate the operators corresponding to the oblique corrections to operators that modify fermion couplings to the gauge bosons as well as operators that modify triple gauge boson couplings. Such identities are simple consequences of the equations of motion. Therefore the contributions from new physics to the oblique parameters can be disguised as modifications of triple gauge boson couplings provided the fermion couplings to the gauge bosons are suitably modified by higher-dimensional operators. Since the experimental constraints on triple gauge boson couplings are much weaker than the constraints on the oblique parameters this observation allows extra room for model building. We derive operator relations in effective theories of the standard model with the electroweak symmetry either linearly or nonlinearly realized and discuss applications of our results.

Lattice QCD with $N_f=2$ flavours of sea quark is used to explore the spectrum and decay of a $J^{PC}=1^{-+}$ spin-exotic hybrid meson. We test lattice determination of $S$-wave decay amplitudes at threshold using $b_1\to \pi \omega$ where agreement with data is found. We find a hybrid meson state at 2.2(2) GeV with a partial width to $\pi b_1$ of 400(120) MeV and to $\pi f_1$ of 90(60) MeV.

The spontaneous breaking of chiral symmetry implies the presence of a short-distance scale in the QCD vacuum, which phenomenologically may be associated with the size of the constituent quark, $\rho \approx 0.3\mathrm{fm}$. We discuss the role of this scale in the matrix elements of the twist-4 and 3 quark-gluon operators determining the leading power ($1/Q^2$)-corrections to the moments of the nucleon spin structure functions. We argue that the flavor-nonsinglet twist-4 matrix element, $f_2^{u-d}$, has a sizable negative value of the order ${\rho }^{-2}$, due to the presence of sea quarks with virtualities $\sim {\rho }^{-2}$ in the proton wave function. The twist-3 matrix element, $d_2$, is not related to the scale ${\rho }^{-2}$. Our arguments support the results of previous calculations of the matrix elements in the instanton vacuum model. We show that this qualitative picture is in agreement with the phenomenological higher-twist correction extracted from an NLO QCD fit to the world data on $g_1^p$ and $g_1^n$, which include recent data from the Jefferson Lab Hall A and COMPASS experiments. We comment on the implications of the short-distance scale $\rho$ for quark-hadron duality and the $x$-dependence of higher-twist contributions.

We derive an effective theory on the orbifold branes of the Randall-Sundrum 1 (RS1) braneworld scenario in the presence of a bulk brane. We concentrate on the regime where the three branes are close and consider a scenario where the bulk brane collides with one of the orbifold branes. This theory allows us to understand the corrections to a low-energy approach due to the presence of higher velocity terms, coming from the Kaluza-Klein modes. We consider the evolution of gravitational waves on a cosmological background and find that, within the large velocity limit, the boundary branes recover a purely four-dimensional behavior.

We construct supergravity plus branes solutions, which we argue to be related to 4d $\mathcal{N}=1$ SQCD with a quartic superpotential. The geometries depend on the ratio $N_f/N_c$ which can be kept of order one, present a good singularity at the origin, and are weakly curved elsewhere. We support our field theory interpretation by studying a variety of features like $R$-symmetry breaking, instantons, Seiberg duality, Wilson loops and pair creation, running of couplings, and domain walls. In a second part of this paper, we address a different problem: the analysis of the interesting physics of different members of a family of supergravity solutions dual to (unflavored) $\mathcal{N}=1$ SYM plus some UV completion.

I argue that string theory compactified on a Riemann surface crosses over at small volume to a higher dimensional background of supercritical string theory. Several concrete measures of the count of degrees of freedom of the theory yield the consistent result that at finite volume, the effective dimensionality is increased by an amount of order $2h/V$ for a surface of genus $h$ and volume $V$ in string units. This arises in part from an exponentially growing density of states of winding modes supported by the fundamental group, and passes an interesting test of modular invariance. Further evidence for a plethora of examples with the spacelike singularity replaced by a higher dimensional phase arises from the fact that the sigma model on a Riemann surface can be naturally completed by many gauged linear sigma models, whose RG flows approximate time evolution in the full string backgrounds arising from this in the limit of large dimensionality. In recent examples of spacelike singularity resolution by tachyon condensation, the singularity is ultimately replaced by a phase with all modes becoming heavy and decoupling. In the present case, the opposite behavior ensues: more light degrees of freedom arise in the small radius regime. We comment on the emerging zoology of cosmological singularities that results.