We explore an ansatz for the QCD vacuum in the Coulomb gauge that describes gauge field fluctuations in the presence of a weakly interacting gas of Abelian monopoles. Such magnetic disorder leads to long-range correlations which are manifested through the area law for the Wilson loop. In particular we focus on the role of the residual monopole-monopole interactions in providing the mechanism for suppression of the gluon propagator at low momenta which also leads to low-momentum enhancement in the ghost propagator.

It has by now been established that standard QCD factorization using transverse momentum dependent parton distribution functions fails in hadroproduction of nearly back-to-back hadrons with high transverse momentum. The essential problem is that gauge-invariant transverse momentum dependent parton distribution functions cannot be defined with process-independent Wilson line operators, thus implying a breakdown of universality. This has led naturally to proposals that a correct approach is to instead use a type of generalized transverse momentum dependent factorization in which the basic factorized structure is assumed to remain valid, but with transverse momentum dependent parton distribution functions that contain nonstandard, process-dependent Wilson line structures. In other words, to recover a factorization formula, it has become common to assume that it is sufficient to simply modify the Wilson lines in the parton correlation functions for each separate hadron. In this paper, we will illustrate by direct counterexample that this is not possible in a non-Abelian gauge theory. Since a proof of generalized transverse momentum dependent factorization should apply generally to any hard hadroproduction process, a single counterexample suffices to show that a general proof does not exist. Therefore, to make the counter-argument clear and explicit, we illustrate with a specific calculation for a double spin asymmetry in a spectator model with a non-Abelian gauge field. The observed breakdown of generalized transverse momentum dependent factorization challenges the notion that the role of parton transverse momentum in such processes can be described using separate correlation functions for each external hadron.

We solve the coupled system of Dyson-Schwinger and Bethe-Salpeter equations for the quark propagator and the pion Bethe-Salpeter amplitude on a finite volume. To this end we use a truncation scheme that includes pion cloud effects in the quark propagator and light mesons. We study volume effects in the quark condensate, the pion mass, and the pion decay constant and compare to corresponding results in other approaches. In general we find large effects for volumes below $V=(1.8\mathrm{fm}{)}^4$.

We study the effect of gluon number fluctuations (Pomeron loops) on the impact parameter behavior of the scattering amplitude in the fixed coupling case. We demonstrate that the dipole-hadron cross section computed from gluon number fluctuations saturates the Froissart bound and the growth of the radius of the black disk with rapidity is enhanced by an additional term as compared to the single event case. We find that the physical amplitude has a Gaussian impact parameter dependence once the gluon number fluctuations are included. This indicates that the fluctuations may be the microscopic origin for the Gaussian impact parameter dependence of the scattering amplitude.

Inspired by the newly observed states $X(4160)$ and $X(3915)$, we analyze the mass spectra of these states in different quark models and calculate their strong decay widths by the ${}^{3}P_0$ model. According to the mass spectra of charmonium states predicted by the potential model, the states ${\chi }_0(3{}^{3}P_0)$, ${\chi }_1(3{}^{3}P_1)$, ${\eta }_{c2}(2{}^{1}D_2)$, ${\eta }_c(4{}^{1}S_0)$ all can be candidates for the $X(4160)$. However, only the decay width of the state ${\eta }_{c2}(2{}^{1}D_2)$ in our calculation is in good agreement with the data reported by Belle, and the decay of ${\eta }_{c2}(2{}^{1}D_2)\to D\overline{D}$, which is not seen in experiment, is also forbidden. Therefore, it is reasonable to interpret the charmonium state ${\eta }_{c2}(2{}^{1}D_2)$ as the state $X(4160)$. For the state $X(3915)$, although the mass of ${\chi }_0(2{}^{3}P_0)$ is compatible with the experimental value, the calculated strong decay width is much larger than experimental data. Hence, the assignment of $X(3915)$ to the charmonium state ${\chi }_0(2{}^{3}P_0)$ is disfavored in our calculation.

In the framework of gauge invariant Stueckelberg approach, totally symmetric arbitrary spin shadow fields in flat space-time of dimension greater than or equal to four are studied. Gauge invariant two-point vertices for such shadow fields are obtained. We demonstrate that, in Stueckelberg gauge frame, these gauge invariant vertices become the standard two-point vertices of CFT. Light-cone gauge two-point vertices of the shadow fields are also obtained. AdS/CFT correspondence for the shadow fields and the non-normalizable solutions of free massless totally symmetric arbitrary spin AdS fields is studied. AdS fields are considered in a modified de Donder gauge and this simplifies considerably the study of AdS/CFT correspondence. We demonstrate that the bulk action, when it is evaluated on solution of the Dirichlet problem, leads to the two-point gauge invariant vertex of shadow field. Also we show that the bulk action evaluated on solution of the Dirichlet problem leads to new description of conformal fields. The new description involves Stueckelberg gauge symmetries and gives simple higher-derivative Lagrangian for the conformal arbitrary spin field. In the Stueckelberg gauge frame, our Lagrangian becomes the standard Lagrangian of conformal field. Light-cone gauge Lagrangian of the arbitrary spin conformal field is also obtained.

We study the internal structure of a non-Abelian vortex in color superconductivity with respect to quark degrees of freedom. Stable non-Abelian vortices appear in the color-flavor-locked phase whose symmetry $SU(3{)}_{\mathrm{c}+\mathrm{L}+\mathrm{R}}$ is further broken to $SU(2{)}_{\mathrm{c}+\mathrm{L}+\mathrm{R}}\otimes U(1{)}_{\mathrm{c}+\mathrm{L}+\mathrm{R}}$ at the vortex cores. Microscopic structure of vortices at scales shorter than the coherence length can be analyzed by the Bogoliubov-de Gennes equation (rather than the Ginzburg-Landau equation). We obtain quark spectra from the Bogoliubov-de Gennes equation by treating the diquark gap having the vortex configuration as a background field. We find that there are massless modes (zero modes) well-localized around a vortex, in the triplet and singlet states of the unbroken symmetry $SU(2{)}_{\mathrm{c}+\mathrm{L}+\mathrm{R}}\otimes U(1{)}_{\mathrm{c}+\mathrm{L}+\mathrm{R}}$. The velocities $v_i$ of the massless modes ($i=t$, $s$ for triplet and singlet) change at finite chemical potential $\mu \ne 0$, and decrease as $\mu$ becomes large. Therefore, low energy excitations in the vicinity of the vortices are effectively described by $1+1$ dimensional massless fermions whose velocities are reduced $v_i<1$.

We describe new on-shell recursion relations for tree amplitudes in $\mathcal{N}=1$ and $\mathcal{N}=2$ gauge theories and use these to show that the structure of the one-loop S-matrix in pure (i.e. without any matter) $\mathcal{N}=1$ and $\mathcal{N}=2$ gauge theories resembles that of pure Yang-Mills theory. We proceed to study gluon scattering in gauge theories coupled to matter in arbitrary representations. The contribution of matter to individual bubble and triangle coefficients can depend on the fourth- and sixth-order indices of the matter representation, respectively. So, the condition that one-loop amplitudes be free of bubbles and triangles can be written as a set of linear Diophantine equations involving these higher-order indices. These equations simplify for supersymmetric theories. We present new examples of supersymmetric theories that have only boxes (and no triangles or bubbles at one-loop) and nonsupersymmetric theories that are free of bubbles. These theories see simplifications in their S-matrices that cannot be deduced just from naive power-counting. In particular, our results indicate that one-loop scattering amplitudes in the $\mathcal{N}=2$, $SU(N)$ theory with a symmetric tensor hypermultiplet and an antisymmetric tensor hypermultiplet are simple like those in the $\mathcal{N}=4$ theory.

We examine numerically the head-on collision of two boosted Schwarzschild black holes, in the realm of Robinson-Trautman spacetimes. Characteristic initial data for the system are constructed and the Robinson-Trautman equation is integrated for these data using a numerical code based on the Galerkin-collocation method. The initial data already have a common horizon so that the evolution covers the post-merger regime up to the final configuration, when the gravitational wave emission ceases. In the nonlinear regime gravitational waves are emitted, extracting mass and linear momentum from the system. The final configuration is a boosted Schwarzschild black hole with rest mass larger than the masses of the two individual initial black holes, and with a smaller final boost parameter characterizing the recoil velocity of the remnant. The efficiency $\Delta$ of the mass-energy extraction by gravitational waves is evaluated. The points $(\Delta ,y)$, where $y$ is the (normalized) rest mass of the remnant black hole, satisfy a nonextensive Tsallis distribution with entropic index $q\simeq 1/2$ for $y\lesssim 12$. Beyond $y\sim 12$ the experimental points deviate from the distribution function and the efficiency presents an absolute maximum for the case of equally massive individual colliding black holes; the remnant has no recoil in this case. By using the Bondi mass formula we also evaluate the total energy $E_W$ carried out by gravitational waves as well as the radiative corrections to the efficiency. $E_W$ increases monotonically with $y$ and the experimental points $(E_W,y)$ also satisfy a nonextensive Tsallis distribution but with $q\simeq 2/3$, up to $y\sim 14.2$. Beyond this value the experimental points increase faster than the distribution function. For any initial infalling velocity $v$, the distribution of momentum of the remnant exhibits a maximum at ${\alpha }_1={\alpha }_m\simeq 0.667$, where ${\alpha }_1$ is related to the ratio of pre-merger rest masses, and has a one-to-one correspondence with $y$ for fixed $v$. Two distinct regimes of gravitational wave emission can be characterized according to (i) ${\alpha }_1<{\alpha }_m$: bursts of gravitational bremsstrahlung; (ii) ${\alpha }_1>{\alpha }_m$: quiescent long time emission of gravitational waves. This picture is also sustained by the analysis of the time behavior of the power emitted ($d{E}_W/du$).

In this paper we continue our study on the accretion process onto superspinning Kerr objects with no event horizon (super-spinars). We discuss the counterpart of the Bondi accretion onto black holes. We first report the results of our numerical simulations. We found a quasi–steady-state configuration for any choice of the parameters of our model. The most interesting feature is the presence of hot outflows. Unlike jets and outflows produced around black holes, which are thought to be powered by magnetic fields and emitted from the poles, here the outflows are produced by the repulsive gravitational force at a small distance from the super-spinar and are ejected around the equatorial plane. In some circumstances, the amount of matter in the outflow is considerable, which can indeed significantly reduce the gas mass accretion rate. Finally, we discuss a possible scenario of the accretion process in more realistic situations, which cannot be simulated by our code.

We derive for applications to isolated systems—on the scale of the Solar System—the first relativistic terms in the $1/c$ expansion of the space time metric $g_{\mu \nu }$ for metric $f(R)$ gravity theories, where $f$ is assumed to be analytic at $R=0$. For our purpose it suffices to take into account up to quadratic terms in the expansion of $f(R)$, thus we can approximate $f(R)=R+a{R}^2$ with a positive dimensional parameter $a$. In the nonrelativistic limit, we get an additional Yukawa correction with coupling strength $G/3$ and Compton wave length $\sqrt{6a}$ to the Newtonian potential, which is a known result in the literature. As an application, we derive to the same order the correction to the geodetic precession of a gyroscope in a gravitational field and the precession of binary pulsars. The result of the Gravity Probe B experiment yields the limit $a\lesssim 5\times {10}^{11}{\mathrm{m}}^2$, whereas for the pulsar B in the PSR J0737-3039 system we get a bound which is about ${10}^4$ times larger. On the other hand the Eöt-Wash experiment provides the best laboratory bound $a\lesssim {10}^{-10}{\mathrm{m}}^2$. Although the former bounds from geodesic precession are much larger than the laboratory ones, they are still meaningful in the case some type of chameleon effect is present and thus the effective values could be different at different length scales.

We derive from first principles, using nonequilibrium field theory, the quantum Boltzmann equations that describe the dynamics of flavor oscillations, collisions, and a time-dependent mass matrix in the early universe. Working to leading nontrivial order in ratios of relevant time scales, we study in detail a toy model for weak-scale baryogenesis: two scalar species that mix through a slowly varying time-dependent and $CP$-violating mass matrix, and interact with a thermal bath. This model clearly illustrates how the $CP$ asymmetry arises through coherent flavor oscillations in a nontrivial background. We solve the Boltzmann equations numerically for the density matrices, investigating the impact of collisions in various regimes.

We explore the possibility that both the weak scale and the thermal relic dark matter abundance are environmentally selected in a multiverse. An underlying supersymmetric theory containing the states of the minimal supersymmetric standard model (MSSM) and singlets, with supersymmetry and $R$ symmetry broken at unified scales, has just two realistic low-energy effective theories. One theory ($\mathrm{SM}+\tilde{w}$) is the standard model augmented only by the wino, having a mass near 3 TeV, and has a Higgs boson mass in the range of (127–142) GeV. The other theory ($\mathrm{SM}+\tilde{h}/\tilde{s}$) has Higgsinos and a singlino added to the standard model. The Higgs boson mass depends on the single new Yukawa coupling of the theory, $y$, and is near 141 GeV for small $y$ but grows to be as large as 210 GeV as this new coupling approaches strong coupling at high energies. Much of the parameter space of this theory will be probed by direct detection searches for dark matter that push 2 orders of magnitude below the present bounds; furthermore, the dark matter mass and cross section on nucleons are correlated with the Higgs boson mass. The indirect detection signal of monochromatic photons from the Galactic center is computed, and the range of parameters that may be accessible to LHC searches for trilepton events is explored. Taking a broader view, allowing the possibility of $R$ symmetry protection to the TeV scale or axion dark matter, we find four more theories: ($\mathrm{SM}+\mathrm{\text{axion}}$), two versions of split supersymmetry, and the E-MSSM, where a little supersymmetric hierarchy is predicted. The special Higgs mass value of $(141\pm 2)\mathrm{GeV}$ appears in symmetry limits of three of the six theories, ($\mathrm{SM}+\mathrm{\text{axion}}$), ($\mathrm{SM}+\tilde{w}$), and ($\mathrm{SM}+\tilde{h}/\tilde{s}$), motivating a comparison of other signals of these three theories.

A classical $SU(2)$ Einstein-Yang-Mills theory in ($3+1$)-dimensional anti–de Sitter spacetime is believed to be dual to a $p$-wave superconductor in ($2+1$)-dimensional flat spacetime. In order to calculate the superconducting coherence length $\xi$ of the holographic superconductor near the superconducting phase transition point, we make a perturbative study of the gravity theory analytically. The superconducting coherence length $\xi$ is found to be proportional to $(1-T/T_c{)}^{-1/2}$ near the critical temperature $T_c$. We also obtain the magnetic penetration depth $\lambda \propto (T_c-T{)}^{1/2}$ by adding a small external homogeneous magnetic field. The results agree with the Ginzburg-Landau theory.

In this paper we build a family of heterotic deformations of the $\mathrm{O}(N)$ sigma model. These deformations break $(1,1)$ supersymmetry down to $(0,1)$ symmetry. We solve this model at large $N$. We also find an alternative superfield formulation of the heterotic ${\mathbb{C}\mathbb{P}}^N$ sigma model, which was discussed in the literature before.

Recently in [Phys. Rev. D 76, 087502 (2007) and Phys. Rev. D 77, 089903 (2008)] a thin-shell wormhole has been introduced in five-dimensional Einstein-Maxwell-Gauss-Bonnet gravity which was supported by normal matter. We wish to consider this solution and investigate its stability. Our analysis shows that for the Gauss-Bonnet parameter $\alpha <0$, stability regions form for a narrow band of finely tuned mass and charge. For the case $\alpha >0$, we iterate once more that no stable, normal matter thin-shell wormhole exists.

We discuss four-dimensional “spatially homogeneous” gravitational instantons. These are self-dual solutions of Euclidean vacuum Einstein equations. They are endowed with a product structure $\mathbb{R}\times {\mathcal{M}}_3$ leading to a foliation into three-dimensional subspaces evolving in Euclidean time. For a large class of homogeneous subspaces, the dynamics coincides with a geometric flow on the three-dimensional slice, driven by the Ricci tensor plus an $\mathfrak{s}\mathfrak{o}(3)$ gauge connection. The flowing metric is related to the vielbein of the subspace, while the gauge field is inherited from the anti-self-dual component of the four-dimensional Levi-Civita connection.

Traditionally, inflationary models are analyzed in terms of parameters such as the scalar spectral index $n_s$ and the tensor to scalar ratio $r$, while dark energy models are studied in terms of the equation of state parameter $w$. Motivated by the fact that both deal with periods of accelerated expansion, we study the evolution of $w$ during inflation, in order to derive observational constraints on its value during an earlier epoch likely dominated by a dynamic form of dark energy. We find that the cosmic microwave background and large-scale structure data is consistent with $w_{\mathrm{inflation}}=-1$ and provides an upper limit of $1+w\lesssim 0.02$. Nonetheless, an exact de Sitter expansion with a constant $w=-1$ is disfavored since this would result in $n_s=1$.

We consider models in which a dark-matter particle decays to a slightly less massive daughter particle and a noninteracting massless particle. The decay gives the daughter particle a small velocity kick. Self-gravitating dark-matter halos that have a virial velocity smaller than this velocity kick may be disrupted by these particle decays, while those with larger virial velocities will be heated. We use numerical simulations to follow the detailed evolution of the total mass and density profile of self-gravitating systems composed of particles that undergo such velocity kicks as a function of the kick speed (relative to the virial velocity) and the decay time (relative to the dynamical time). We show how these decays will affect the halo mass-concentration relation and mass function. Using measurements of the halo mass-concentration relation and galaxy-cluster mass function to constrain the lifetime–kick-velocity parameter space for decaying dark matter, we find roughly that the observations rule out the combination of kick velocities greater than $100\mathrm{km}{\mathrm{s}}^{-1}$ and decay times less than a few times the age of the Universe.