The recent weak-lensing measurement of the dark matter mass of the high-redshift galaxy cluster XMMUJ2235.3-2557 of $(8.5\pm 1.7)\times {10}^{14}{M}_{\odot }$ at $z=1.4$, indicates that, if the cluster is assumed to be the result of the collapse of dark matter in a primordial Gaussian field in the standard lambda cold dark matter model, then its abundance should be $<2\times {10}^{-3}$ clusters in the observed area. Here we investigate how to boost the probability of XMMUJ2235.3-2557, in particular, resorting to deviations from Gaussian initial conditions. We show that this abundance can be boosted by factors $>3–10$ if the non-Gaussianity parameter $f_{\mathrm{NL}}^{\mathrm{local}}$ is in the range 150–200. This value is comparable to the limit for $f_{\mathrm{NL}}$ obtained by current constraints from the cosmic microwave background. We conclude that mass determination of high-redshift, massive clusters can offer a complementary probe of primordial non-Gaussianity.

We consider a deformation of the ${\mathrm{AdS}}_5\times S^5$ solution of IIB supergravity obtained by taking the boundary value of the dilaton to be time dependent. The time dependence is taken to be slowly varying on the anti-de Sitter (AdS) scale thereby introducing a small parameter $ϵ$. The boundary dilaton has a profile which asymptotes to a constant in the far past and future and attains a minimum value at intermediate times. We construct the supergravity (sugra) solution to first nontrivial order in $ϵ$, and find that it is smooth, horizon-free, and asymptotically ${\mathrm{AdS}}_5\times S^5$ in the far future. When the intermediate values of the dilaton becomes small enough the curvature becomes of order the string scale and the sugra approximation breaks down. The resulting dynamics is analyzed in the dual $SU(N)$ gauge theory on $S^3$ with a time dependent coupling constant which varies slowly. When $Nϵ\ll 1$, we find that a quantum adiabatic approximation is applicable, and use it to argue that at late times the geometry becomes smooth ${\mathrm{AdS}}_5\times S^5$ again. When $Nϵ\gg 1$, we formulate a classical adiabatic perturbation theory based on coherent states which arises in the large $N$ limit. For large values of the ’t Hooft coupling this reproduces the supergravity results. For small ’t Hooft coupling the coherent state calculations become involved and we cannot reach a definite conclusion. We argue that the final state should have a dual description which is mostly smooth ${\mathrm{AdS}}_5$ space with the possible presence of a small black hole.

We consider the emission of two closed string tachyons from a decaying $\mathrm{D}p$-brane in bosonic string theory. We study the high-energy limit of the emission amplitude by using an analogue to electrostatics. The case where the emitted strings have equal energies is analyzed in detail, and we obtain a relatively simple result for the emission amplitude. We identify expected poles for $s$- and $t$-channel emission. In the high-energy limit, the amplitude decays exponentially ($\sim e^{-2\pi \omega }$) or faster in the energies $\omega$ of the closed strings.

We give a detailed account of the construction of nontrivial localized solutions in a $2+1$ dimensional model of superconductors using a $3+1$ dimensional gravitational dual theory of a black hole coupled to a scalar field. The solutions are found in the presence of a background magnetic field. We use numerical and analytic techniques to solve the full Maxwell-scalar equations of motion in the background geometry, finding condensate droplet solutions, and vortex solutions possessing a conserved winding number. These solutions and their properties, which we uncover, help shed light on key features of the $(B,T)$ phase diagram.

Recently it has been advocated [A. G. Cohen and S. L. Glashow, Phys. Rev. Lett. 97, 021601 (2006)] that for describing nature within the minimal symmetry requirement, certain subgroups of the Lorentz group may play a fundamental role. One such group is $E(2)$ which induces a Lie algebraic noncommutative spacetime [M. M. Sheikh-Jabbari and A. Tureanu, Phys. Rev. Lett. 101, 261601 (2008); arXiv:0811.3670] where translation invariance is not fully maintained. We have constructed a consistent structure of noncommutative phase space for this system, and furthermore we have studied an appropriate point particle action on it. Interestingly, the Einstein dispersion relation $p^2=m^2$ remains intact. The model is constructed by exploiting a dual canonical phase space following the scheme developed by us earlier [S. Ghosh and P. Pal, Phys. Rev. D 75, 105021 (2007)].

For massive gravity in a de Sitter background one encounters problems of stability when the curvature is larger than the graviton mass. I analyze this situation from the path integral point of view and show that it is related to the conformal factor problem of Euclidean quantum (massless) gravity. When a constraint for massive gravity is incorporated and the proper treatment of the path integral measure is taken into account one finds that, for particular choices of the DeWitt metric on the space of metrics (in fact, the same choices as in the massless case), one obtains the opposite bound on the graviton mass.

In this paper the dynamics of Schwarzschild null geodesics in the context of low-energy effective field theories incorporating some interactions violating the equivalence principle is examined. Nonperturbed geodesics are expressed in terms of a convenient set of constants called orbital elements. The modifications introduced by the effective interactions are treated as small perturbations, then the method of variation of parameters is employed to find the evolution of the orbital elements for the true worldlines. We next focus our discussion on the geometry of nondispersive photon orbits and highlight the importance of different orbital elements in long-term change of the orbit. This calculation shows that nondispersive forces acting on null geodesics drive a secular growth of the positional elements. As an application of our results we examine the evolution of mean orbital elements in the semiclassical theory of quantum gravitational optics and show that the averaged correction terms are within the range of the uncertainty principle.

The Gauss-Codazzi method is used to discuss the gravitational collapse of a charged Reisner-Nordström domain wall. We solve the classical equations of motion of a thin charged shell moving under the influence of its own gravitational field and show that a form of cosmic censorship applies. If the charge of the collapsing shell is greater than its mass, then the collapse does not form a black hole. Instead, after reaching some minimal radius, the shell bounces back. The Schrödinger canonical formalism is used to quantize the motion of the charged shell. The limits near the horizon and near the singularity are explored. Near the horizon, the Schrödinger equation describing evolution of the collapsing shell takes the form of the massive wave equation with a position dependent mass. The outgoing and incoming modes of the solution are related by the Bogolubov transformation which precisely gives the Hawking temperature. Near the classical singularity, the Schrödinger equation becomes nonlocal, but the wave function describing the system is nonsingular. This indicates that while quantum effects may be able to remove the classical singularity, it may also introduce some new effects.

We discuss some hitherto puzzling features of the small-scale structure of cosmic strings. We argue that kinks play a key role, and that an important quantity to study is their sharpness distribution. In particular we suggest that for very small scales the two-point correlation function of the string tangent vector varies linearly with the separation and not as a fractional power, as proposed by Polchinski and Rocha [Phys. Rev. D 74, 083504 (2006)]. However, our results are consistent with theirs, because the range of scales to which this linearity applies shrinks as evolution proceeds.

Based on the ${\mathbf{Z}}_{12-I}$ orbifold compactification of heterotic string theory, we construct a flipped-SU(5) model with three families of standard model matter and ingredients for dynamical supersymmetry breaking through the hidden sector matter ${\overline{\mathbf{10}}}^{\prime }$ and ${\mathbf{5}}^{\prime }$ of $\mathrm{SU}(5{)}^{\prime }$, which are neutral under the visible sector flipped-SU(5). The appearance of one chiral set ${\overline{\mathbf{10}}}^{\prime }$ and ${\mathbf{5}}^{\prime }$ is the new feature of the present flipped-SU(5) string model with ${sin}^2{\theta }_W^0=\frac{3}{8}$. As required, all the exotic states are shown to decouple from low energy physics. Above the compactification scale, the flipped-SU(5) gauge symmetry is enhanced to SO(10) gauge symmetry by including the Kaluza-Klein modes. The threshold correction is calculated by counting Kaluza-Klein modes, and we show that the model allows a very wide range for the hidden-sector confining scale (${10}^{11}\mathrm{GeV}–{10}^{16}\mathrm{GeV}$).

We construct a model of spontaneous $CP$ violation in ${\mathrm{E}}_6$ supersymmetric grand unified theory. In the model, we employ an $\mathrm{SU}(2{)}_{\mathrm{F}}$ flavor symmetry and an anomalous $\mathrm{U}(1{)}_{\mathrm{A}}$ symmetry. The $\mathrm{SU}(2{)}_{\mathrm{F}}$ flavor symmetry is introduced to provide the origin of hierarchical structures of Yukawa coupling and to ensure the universality of sfermion soft masses. The anomalous $\mathrm{U}(1{)}_{\mathrm{A}}$ symmetry is introduced to realize the doublet-triplet mass splitting, to provide the origin of hierarchical structures of Yukawa couplings, and to solve the $\mu$ problem. In the model, $CP$ is spontaneously broken by the $\mathrm{SU}(2{)}_{\mathrm{F}}$ breaking in order to provide a Kobayashi-Maskawa phase and to evade the supersymmetric $CP$ problem. However, a naive construction of the model generally leads to an unwanted outcome, $\arg [\mu b^{*}]=\mathcal{O}(1)$, when $CP$ violating effects in the flavor sector are taken into account. We cure this difficulty by imposing a discrete symmetry and find that this prescription can play additional roles. It ensures that the realistic up-quark mass and Cabibbo angle are simultaneously realized without cancellation between $\mathcal{O}(1)$ coefficients. Also, severe constraints from the chromo-electric dipole moment of the quark can be satisfied without destabilizing the weak scale. The discrete symmetry reduces the number of free parameters, but the model is capable of reproducing quark and lepton mass spectra, mixing angles, and a Jarlskog invariant. We obtain characteristic predictions $V_{ub}\sim \mathcal{O}({\lambda }^4)$ ($\lambda =0.22$) and $|V_{cb}{Y}_b|=|Y_c|$ at the grand unified theory scale.

We present a calculation of the $K_{\ell 3}$ transition form factors using the AdS/QCD correspondence. We also solidify and extend our ability to calculate quantities in the flavor-broken versions of AdS/QCD. The normalization of the form factors is a crucial ingredient for extracting $|V_{us}|$ from data, and the results obtained here agree well with results from chiral perturbation theory and lattice gauge theory. The slopes and curvature of the form factors agree well with the data, and with what results are available from other methods of calculation.

We study the gluon propagator $D_{\mu \nu }^{ab}(x)$ in the Landau gauge in SU(3) lattice QCD at $\beta =5.7$, 5.8, and 6.0 at the quenched level. The effective gluon mass is estimated as $400–600\mathrm{MeV}$ for $r\equiv (x_{\alpha }{x}_{\alpha }{)}^{1/2}=0.5–1.0\mathrm{fm}$. Through the functional-form analysis of $D_{\mu \nu }^{ab}(x)$ obtained in lattice QCD, we find that the Landau-gauge gluon propagator $D_{\mu \mu }^{aa}(r)$ is well described by the Yukawa-type function $e^{-mr}/r$ with $m\simeq 600\mathrm{MeV}$ for $r=0.1–1.0\mathrm{fm}$ in the four-dimensional Euclidean space-time. In the momentum space, the gluon propagator ${\tilde{D}}_{\mu \mu }^{aa}(p^2)$ with $(p^2{)}^{1/2}=0.5–3\mathrm{GeV}$ is found to be well approximated with a new-type propagator of $(p^2+m^2{)}^{-3/2}$, which corresponds to the four-dimensional Yukawa-type propagator. Associated with the Yukawa-type gluon propagator, we derive analytical expressions for the zero-spatial-momentum propagator $D_0(t)$, the effective mass $M_{\mathrm{eff}}(t)$, and the spectral function $\rho (\omega )$ of the gluon field. The mass parameter $m$ turns out to be the effective gluon mass in the infrared region of $\sim 1\mathrm{fm}$. As a remarkable fact, the obtained gluon spectral function $\rho (\omega )$ is almost negative definite for $\omega >m$, except for a positive $\delta$-functional peak at $\omega =m$.

We present the calculations of the complete next-to-leading order (NLO) QCD effects on the single top productions induced by model-independent $tqg$ flavor-changing neutral-current couplings at hadron colliders. Our results show that, for the $tcg$ coupling, the NLO QCD corrections can enhance the total cross sections by about 60% and 30%, and for the $tug$ coupling by about 50% and 20% at the Tevatron and LHC, respectively, which means that the NLO corrections can increase the experimental sensitivity to the flavor-changing neutral-current couplings by about $10\%–30\%$. Moreover, the NLO corrections reduce the dependence of the total cross sections on the renormalization or factorization scale significantly, which lead to increased confidence on the theoretical predictions. Besides, we also evaluate the NLO corrections to several important kinematic distributions, and find that for most of them the NLO corrections are almost the same and do not change the shape of the distributions.

We study the production of prompt diphotons in the central region of rapidity within the framework of the quasi-multi-Regge-kinematic approach applying the hypothesis of quark and gluon Reggeization. We describe accurately and without free parameters the experimental data which were obtained by the CDF Collaboration at the Tevatron collider. It is shown that the main contribution to the studied process is given by the direct fusion of two Reggeized gluons into a photon pair, which is described by the effective Reggeon-Reggeon to particle-particle vertex. The contribution from the annihilation of Reggeized quark-antiquark pair into a diphoton is also considered. At the stage of numerical calculations we use the Kimber-Martin-Ryskin prescription for unintegrated quark and gluon distribution functions, with the Martin-Roberts-Stirling-Thorne collinear-parton densities for a proton as input.

The matter effects for solar neutrino oscillations are studied in a general scheme with an arbitrary number of sterile neutrinos, without any constraint on the mixing, assuming only a realistic hierarchy of neutrino squared-mass differences in which the smallest squared-mass difference is effective in solar neutrino oscillations. The validity of the analytic results are illustrated with a numerical solution of the evolution equation in three examples of the possible mixing matrix in the simplest case of four-neutrino mixing.

We parametrize the initial flux composition of high energy astrophysical neutrinos as $({\Phi }_e^0:{\Phi }_{\mu }^0:{\Phi }_{\tau }^0)=(1:n:0)$, where $n$ characterizes the source. All usually assumed neutrino sources appear as limits of this simple parametrization. We investigate how precise neutrino telescopes can pin down the value of $n$. We furthermore show that there is a neutrino mixing scenario in which the ratio of muon neutrinos to the other neutrinos takes a constant value regardless of the initial flux composition. This occurs when the muon neutrino survival probability takes its minimal allowed value. The phenomenological consequences of this very predictive neutrino mixing scenario are given.

In a recent Brief Report by Shalaby, a new first-order perturbative calculation of the metric operator for an $i{\varphi }^3$ scalar field theory is given. It is claimed that the incorporation of derivative terms in the ansatz for the metric operator results in a local solution, in contrast to the nonlocal solution previously obtained by Bender, Brody, and Jones. Unfortunately, Shalaby’s calculation is not valid because of sign errors.

We prove the analyticity of the finite volume QCD partition function for complex values of the $\theta$-vacuum parameter. The absence of singularities different from Lee-Yang zeros only permits $\wedge$ cusp singularities in the vacuum energy density and never $\vee$ cusps. This fact together with the Vafa-Witten diamagnetic inequality implies the vanishing of the density of Lee-Yang zeros at $\vartheta =0$ and has an important consequence: the absence of a first order phase transition at $\theta =0$. The result provides a key missing link in the Vafa-Witten proof of parity symmetry conservation in vectorlike gauge theories and follows from renormalizability, unitarity, positivity, and existence of Bogomol’nyi-Prasad-Sommerfield bounds. Generalizations of this theorem to other physical systems are also discussed, with particular interest focused on the nonlinear ${\mathbb{C}\mathbb{P}}^N$ sigma model.

We study a gauge/gravity model for the thermodynamics of a gauge theory with one running coupling. The gravity side contains an ansatz for the metric and a scalar field; on the field theory side one starts by giving an ansatz for the beta function describing the scale dependence of the coupling. The model is based on relating the scale to the extra dimensional coordinate and the beta function to the gravity fields, thereby also determining the scalar field potential. We study three different forms of beta functions of increasing complexity and give semianalytic solutions describing first order or continuous transitions.