In many models of gauged Q-balls, which were studied in the literature, there are upper limits for charge $Q$ (and size) of Q-balls due to repulsive Coulomb force. The only known model that allows large $Q$ without limitation is the V-shaped potential, $V\propto |\varphi |$, which is singular at $\varphi =0$. To make it clear whether the property of unlimited $Q$ is peculiar to the singular potential, we derive general conditions for potentials that allow Q-balls with unbounded $Q$. We find that large gauged $Q$-balls exist even for regular potentials. One of the simple models is $V=({\mu }^2/2){\varphi }^2[1+K\ln (\varphi /M{)}^2]$ with $K<0$. We investigate equilibrium solutions for this model systematically. As the electric charge $Q$ increases, the field configuration of the scalar field becomes shell-like; because the charge is concentrated on the surface, the Coulomb force does not destroy the Q-ball configuration. These properties are analogous to those in the V-shaped model. We also find that for each $K$ there is another sequence of unstable solutions, which is separated from the other sequence of the stable solutions. As $|K|$ increases, the two sequences approach; eventually at some point in $-1.07<K<-1.06$, the “recombination” of the two sequences takes place.

For a given quantum field theory, provided the area of the entangling surface is fixed, what surface maximizes entanglement entropy? We analyze the answer to this question in four and higher dimensions. Surprisingly, in four dimensions the answer is related to a mathematical problem of finding surfaces that minimize the Willmore (bending) energy and eventually to the Willmore conjecture. We propose a generalization of the Willmore energy in higher dimensions and analyze its minimizers in a general class of topologies $S^m\times S^n$ and make certain observations and conjectures that may have some mathematical significance.

We present the geometry of spacetimes that are tangentially approximated by de Sitter spaces whose cosmological constants vary over spacetime. Cartan geometry provides one with the tools to describe manifolds that reduce to a homogeneous Klein space at the infinitesimal level. We consider a Cartan geometry in which the underlying Klein space is at each point a de Sitter space, for which the combined set of pseudoradii forms a nonconstant function on spacetime. We show that the torsion of such a geometry receives a contribution that is not present for a cosmological constant. The structure group of the obtained de Sitter–Cartan geometry is by construction the Lorentz group $SO(1,3)$. Invoking the theory of nonlinear realizations, we extend the class of symmetries to the enclosing de Sitter group $SO(1,4)$, and compute the corresponding spin connection, vierbein, curvature, and torsion.

We investigate the cosmological applications of $F(T,T_G)$ gravity, which is a novel modified gravitational theory based on the torsion invariant $T$ and the teleparallel equivalent of the Gauss-Bonnet term $T_G$. $F(T,T_G)$ gravity differs from both $F(T)$ theories as well as from $F(R,G)$ class of curvature modified gravity, and thus its corresponding cosmology proves to be very interesting. In particular, it provides a unified description of the cosmological history from early-times inflation to late-times self-acceleration, without the inclusion of a cosmological constant. Moreover, the dark energy equation-of-state parameter can be quintessence or phantomlike, or experience the phantom-divide crossing, depending on the parameters of the model.

Inspired by the teleparallel formulation of general relativity, whose Lagrangian is the torsion invariant $T$, we have constructed the teleparallel equivalent of Gauss-Bonnet gravity in arbitrary dimensions. Without imposing the Weitzenböck connection, we have extracted the torsion invariant $T_G$, equivalent (up to boundary terms) to the Gauss-Bonnet term $G$. $T_G$ is constructed by the vielbein and the connection, it contains quartic powers of the torsion tensor, it is diffeomorphism and Lorentz invariant, and in four dimensions it reduces to a topological invariant as expected. Imposing the Weitzenböck connection, $T_G$ depends only on the vielbein, and this allows us to consider a novel class of modified gravity theories based on $F(T,T_G)$, which is not spanned by the class of $F(T)$ theories, nor by the $F(R,G)$ class of curvature modified gravity. Finally, varying the action we extract the equations of motion for $F(T,T_G)$ gravity.

We present a simple holographic model of an insulator. Unlike most previous holographic insulators, the zero temperature infrared geometry is completely nonsingular. Both the low temperature DC conductivity and the optical conductivity at zero temperature satisfy power laws with the same exponent, given by the scaling dimension of an operator in the IR. Changing a parameter in the model converts it from an insulator to a conductor with a standard Drude peak.

The emergence of the seeds of cosmic structure, from a perfect isotropic and homogeneous Universe, has not been clearly explained by the standard version of inflationary models as the dynamics involved preserve the homogeneity and isotropy at all times. A proposal that attempts to deal with this problem, by introducing “the self-induced collapse hypothesis,” has been introduced by D. Sudarsky and collaborators in previous papers. In all these works, the collapse of the wave function of the inflaton mode is restricted to occur during the inflationary period. In this paper, we analyze the possibility that the collapse happens during the radiation era. A viable model can be constructed under the condition that the inflaton field variable must be affected by the collapse while the momentum variable can or cannot be affected. Another condition to be fulfilled is that the time of collapse must be independent of $k$. However, when comparing with recent observational data, the predictions of the model cannot be distinguished from the ones provided by the standard inflationary scenario. The main reason for this arises from the requirement that primordial power spectrum obtained for the radiation era matches the amplitude of scalar fluctuations consistent with the latest cosmic microwave background observations. This latter constraint results in a limit on the possible times of collapse and ensures that the contribution of the inflaton field to the energy-momentum tensor is negligible compared to the contribution of the radiation fields.

The minimal supersymmetry standard model (MSSM) extended with vectorlike theories have long been discussed. If we extend the vectorlike MSSM theory into NMSSM and let the vectorlike particles couple with the singlet (S), we find out a natural way to generate the vectorlike particle masses near 1 TeV through the breaking of the $Z_3$ group. Compared with the $\text{MSSM}+\text{vectorlike}$ models, vectorlike models extended into NMSSM contain more Yukawa couplings and can help us adjust the renormalization group (RG) trajectories of the gauge couplings in order to unify the intersections. They can also help press down the gauge RG-$\beta$ functions for a $5+\overline{5}+10+\overline{10}$ model, in order for the RG trajectories of the gauge couplings to unify before the Landau pole. We also discuss the Higgs mass contributed from the vectorlike sectors in this case.

We investigate the order of the finite temperature chiral symmetry restoration transition for QCD with two massless fermions, by using a novel method, based on simulating imaginary values of the quark chemical potential $\mu =i{\mu }_i$, ${\mu }_i\in \mathbb{R}$. Our method exploits the fact that, for low enough quark mass $m$ and large enough chemical potential ${\mu }_i$, the chiral transition is decidedly first order, then turning into crossover at a critical mass $m_c(\mu )$. It is thus possible to determine the critical line in the $m-{\mu }^2$ plane, which can be safely extrapolated to the chiral limit by taking advantage of the known tricritical indices governing its shape. We test this method with standard staggered fermions and the result of our simulations is that $m_c(\mu =0)$ is positive, so that the phase transition at zero density is definitely first order in the chiral limit, on our coarse $N_t=4$ lattices with $a\simeq 0.3\mathrm{fm}$.

We calculate the mass of the Higgs boson in the standard model in terms of the underlying Lagrangian parameters at complete 2-loop order with leading 3-loop corrections. A computer program implementing the results is provided. The program also computes and minimizes the standard model effective potential in Landau gauge at 2-loop order with leading 3-loop corrections.

We study the process $e^{-}{e}^{+}\to ZH$ where $H$ represents the standard model (SM) Higgs particle $H_{\mathrm{SM}}$, or the minimal supersymmetric standard model (MSSM) ones $h^0$ and $H^0$. In each case, we compute the one-loop effects and establish very simple expressions, called supersimple (sim), for the helicity-conserving (dominant) and the helicity-violating (suppressed) amplitudes. Such expressions are then used to construct various cross sections and asymmetries, involving polarized or unpolarized beams and Z-polarization measurements. We examine the adequacy of such expressions to distinguish SM from MSSM effects or from other types of beyond the standard model contributions.

The ATLAS detector at the Large Hadron Collider is used to search for the lepton flavor violating process $Z\to e\mu$ in $pp$ collisions using $20.3{\mathrm{fb}}^{-1}$ of data collected at $\sqrt{s}=8\mathrm{TeV}$. An enhancement in the $e\mu$ invariant mass spectrum is searched for at the $Z$-boson mass. The number of $Z$ bosons produced in the data sample is estimated using events of similar topology, $Z\to ee$ and $\mu \mu$, significantly reducing the systematic uncertainty in the measurement. There is no evidence of an enhancement at the $Z$-boson mass, resulting in an upper limit on the branching fraction, $\mathcal{B}(Z\to e\mu )<7.5\times 10^{-7}$ at the 95% confidence level.

We propose a new and realistic 3-3-1 model with the minimal lepton and scalar contents, named the simple 3-3-1 model. The scalar sector contains two new heavy Higgs bosons—one neutral $H$ and another singly charged $H^{\pm }$—besides the standard-model Higgs boson. There is a mixing between the $Z$ boson and the new neutral gauge boson ($Z^{\prime }$). The $\rho$ parameter constrains the 3-3-1 breaking scale ($w$) to be $w>460\mathrm{GeV}$. The quarks get consistent masses via five-dimensional effective interactions, while the leptons do so via interactions up to six dimensions. Particularly, the neutrino small masses are generated as a consequence of the approximate lepton-number symmetry of the model. The proton is stabilized due to the lepton parity conservation $(-1{)}^L$. The hadronic flavor-changing neutral currents are calculated, giving a bound $w>3.6\mathrm{TeV}$, and yield that the third quark generation is different from the first two. The correct mass generation for the top quark implies that the minimal scalar sector as proposed is unique. By the simple 3-3-1 model, the other scalars besides the minimal ones can behave as inert fields responsible for dark matter. A triplet, doublet, and singlet dark matter are respectively recognized. Our proposals provide the solutions for the long-standing dark matter issue in the minimal 3-3-1 model.

We study deep inelastic scattering at large ’t Hooft coupling and finite $x$ from gauge/string duality beyond single-hadron final states, which gives the leading large-$N_c$ contribution. Within the supergravity approximation, we calculate the subleading large-$N_c$ contribution by introducing an extra hadron into the final states. We find that the contribution from these double-hadron final states will dominate in the Bjorken limit $q^2\to \infty$ compared with the single-hadron states. We discuss the implications of our results.

A reliable evaluation of the integral giving the hadronic vacuum polarization contribution to the muon anomalous magnetic moment should be possible using a simple trapezoid rule integration of lattice data for the subtracted electromagnetic current polarization function in the Euclidean momentum interval $Q^2>Q_{\min }^2$, coupled with an $N$-parameter Padé or other representation of the polarization in the interval $0<Q^2<Q_{\min }^2$, for sufficiently high $Q_{\min }^2$ and sufficiently large $N$. Using a physically motivated model for the $I=1$ polarization, and the covariance matrix from a recent lattice simulation to generate associated fake “lattice data,” we show that systematic errors associated with the choices of $Q_{\min }^2$ and $N$ can be reduced to well below the 1% level for $Q_{\min }^2$ as low as $0.1{\mathrm{GeV}}^2$ and rather small $N$. For such low $Q_{\min }^2$, both a next-to-next-to-leading-order (NNLO) chiral representation with one additional NNNLO term and a low-order polynomial expansion employing a conformally transformed variable also provide representations sufficiently accurate to reach this precision for the low-$Q^2$ contribution. Combined with standard techniques for reducing other sources of error on the lattice determination, this hybrid strategy thus looks to provide a promising approach to reaching the goal of a subpercent-precision determination of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment on the lattice.

Neutrino capture on tritium has emerged as a promising method for detecting the cosmic neutrino background ($\mathrm{C}\nu \mathrm{B}$). We show that relic neutrinos are captured most readily when their spin vectors are antialigned with the polarization axis of the tritium nuclei and when they approach along the direction of polarization. As a result, $\mathrm{C}\nu \mathrm{B}$ observatories may measure anisotropies in the cosmic neutrino velocity and spin distributions by polarizing the tritium targets. A small dipole anisotropy in the $\mathrm{C}\nu \mathrm{B}$ is expected due to the peculiar velocity of the lab frame with respect to the cosmic frame and due to late-time gravitational effects. The PTOLEMY experiment, a tritium observatory currently under construction, should observe a nearly isotropic background. This would serve as a strong test of the cosmological origin of a potential signal. The polarized-target measurements may also constrain nonstandard neutrino interactions that would induce larger anisotropies and help discriminate between Majorana versus Dirac neutrinos.

The effective strength of electromagnetism interactions can be controlled by confining the fields to a cavity and these effects might be used to push graphene into a strongly coupled regime. We study the similar D3/probe D5 system on a compact space and discuss the gravity dual for a cavity between two mirrors. We show that the introduction of a conformal symmetry breaking length scale introduces a mass gap on a single D5 sheet. Bilayer configurations display exciton condensation between the sheets. There is a first-order phase transition away from the exciton condensate if a strong enough magnetic field is applied. We finally map out the phase structure of these systems in a cavity with the presence of mirror reflections of the probes—a mass gap may form through exciton condensation with the mirror image.

In this paper we have extended a three-dimensional approach for describing quark-antiquark bound states based on a momentum-helicity representation. To this end we have formulated the relativistic form of the Lippmann-Schwinger equation in the momentum-helicity space which leads to integral equations with one variable. Then we have solved these integral equations by inserting a spin-dependent quark-antiquark potential model numerically. Finally we have obtained the mass spectrum of light mesons and we have compared these results with the results which are obtained in the partial wave representation.

We calculate the electroweak sphaleron rates in the reduced minimal 3-3-1 (RM331) model. In the context of the early Universe, this model undergoes a sequence of two first-order phase transitions, $SU(3)\to SU(2)$ at the TeV scale and $SU(2)\to U(1)$ at the $10^2\mathrm{GeV}$ scale, as the Universe cools down from the hot big bang. By a thin-wall approximation, we show that for each phase transition in this sequence, the sphaleron rate is larger than the cosmological expansion rate at temperatures higher than the critical temperature, and after the phase transition, the sphaleron process is decoupled. This may provide the baryon-number violation (B violation) necessary for baryogenesis in the relationship with nonequilibrium physics in the early Universe.

Binary neutron stars in circular orbits can be modeled as helically symmetric, i.e., stationary in a rotating frame. This symmetry gives rise to a first integral of the Euler equation, often employed for constructing equilibrium solutions via iteration. For eccentric orbits, however, the lack of helical symmetry has prevented the use of this method, and the numerical relativity community has often resorted to constructing initial data by superimposing boosted spherical stars without solving the Euler equation. The spuriously excited neutron star oscillations seen in evolutions of such data arise because such configurations lack the appropriate tidal deformations and are stationary in a linearly comoving—rather than rotating—frame. We consider eccentric configurations at apoapsis that are instantaneously stationary in a rotating frame. We extend the notion of helical symmetry to eccentric orbits, by approximating the elliptical orbit of each companion as instantaneously circular, using the ellipse’s inscribed circle. The two inscribed helical symmetry vectors give rise to approximate instantaneous first integrals of the Euler equation throughout each companion. We use these integrals as the basis of a self-consistent iteration of the Einstein constraints to construct conformal thin-sandwich initial data for eccentric binaries. We find that the spurious stellar oscillations are reduced by at least an order of magnitude, compared with those found in evolutions of superposed initial data. The tidally induced oscillations, however, are physical and qualitatively similar to earlier evolutions. Finally, we show how to incorporate radial velocity due to radiation reaction in our inscribed helical symmetry vectors, which would allow one to obtain truly noneccentric initial data when our eccentricity parameter $e$ is set to zero.