International Journal of Modern Physics A

From the underlying nonlinear realisation, we compute the complete E${}_{11}$ invariant equations of motion in eleven dimensions, at the linearised level, up to and including level four in the fields. Thus, we include the metric, the three and six forms, the dual graviton and three fields at level four. The fields are linked by a set of duality equations, which are first-order in derivatives and transform into each other under the E${}_{11}$ symmetries. From these duality relations, we deduce second-order equations of motion, including those for the usual supergravity fields. As a result the on-shell degrees of freedom are those of the eleven-dimensional supergravity. We also show that the level four fields provide an eleven-dimensional origin of Romans theory and lead to a novel duality relation.

Quantum M-theory is formulated using the current algebra technique. The current algebra is based on a Kac–Moody algebra rather than usual finite dimensional Lie algebra. Specifically, I study the $E_{11}$ Kac–Moody algebra that was shown recently${}^{1-5}$ to contain all the ingredients of M-theory. Both the internal symmetry and the external Lorentz symmetry can be realized inside $E_{11}$, so that, by constructing the current algebra of $E_{11}$, I obtain both internal gauge theory and gravity theory. The energy–momentum tensor is constructed as the bilinear form of the currents, yielding a system of quantum equations of motion of the currents/fields. Supersymmetry is incorporated in a natural way. The so-called “field-current identity” is built in and, for example, the gravitino field is itself a conserved supercurrent. One unanticipated outcome is that the quantum gravity equation is not identical to the one obtained from the Einstein–Hilbert action.

A “ground-up” Higgs Factory design methodology is described. For concreteness, numerical parameter choices are drawn primarily from CEPC, the Circular Electron Positron Collider. The goals are to find: (i) optimal parameters, (ii) improved understanding , (iii) a tentative lattice design. As illustration of the method, six chromaticity-corrected lattices, with cell lengths ranging from 45 m to 280 m, all with identical ${\beta }_y=2$ mm or ${\beta }_y=10$ mm intersection region optics, are designed and their properties compared. For simplicity only a single “toy ring,” circumference (76 km), with one interaction point, and a single beam energy (120 GeV) is considered. For the cell-length optimization a figure of merit FOM (essentially integrated luminosity) is maximized consistent with a dimensionless “fine tuning penalty function” or figure of demerit FOD not being allowed to exceed a conservatively chosen upper limit. The tentative recommendation from this investigation is that the optimal CEPC route is (except for obvious changes) to simply copy LEP: 80 m cell length and two-in-one single-ring operation. The main luminosity-increasing improvements are increased radius and power, top-off-full-energy-injection, noninterleaved sextupoles, more than 100 beam bunch operation, and improved intersection region design. Local chromaticity compensation (with its inevitable intense hard X-rays incident on the detectors) is found to be unnecessary. With these changes luminosity in excess of $10^{34}{\mathrm{\text{cm}}}^{-2}{\mathrm{\text{s}}}^{-1}$ is projected to be achievable.

In this paper, we will use a BIonic solution for analyzing the holographic cosmology. A BIonic solution is a configuration of a D3-brane and an anti-D3-brane connected by a wormhole, and holographic cosmology is a recent proposal to explain cosmic expansion by using the holographic principle. In our model, a BIonic configuration will be produced by the transition of fundamental black strings. The formation of a BIonic configuration will cause inflation. As the D3-brane moves away from the anti-D3-brane, the wormhole will get annihilated, and the inflation will end with the annihilation of this wormhole. However, it is possible for a D3-brane to collide with an anti-D3-brane. Such a collision will occur if the distance between the D3-brane and the anti-D3-brane reduces, and this will create tachyonic states. We will demonstrate that these tachyonic states will lead to the formation of a new wormhole, and this will cause acceleration of the universe before such a collision.

It has been shown in the literature that effective gravitational constants, which are derived from Verlinde’s formalism, can be used to introduce the Tsallis and Kaniadakis statistics. This method provides a simple alternative to the usual procedure normally used in these non-Gaussian statistics. We have applied our formalism in both Jeans mass criterion of stability and the free fall time collapsing of a self-gravitating system where new results were obtained. A possible connection between our formalism and deviations of Newton’s law of gravitation in a submillimeter range was carried out.

Experimental data on transverse momentum spectra of strange particles $(K_S^0,K^{-},K^{\ast 0},\varphi ,\mathrm{\Lambda },{\mathrm{\Lambda }}^{\ast },{\mathrm{\Sigma }}^{\ast },{\mathrm{\Xi }}^{-},\mathrm{\Omega })$ produced in $pp$ collisions at $\sqrt{s}=200\mathrm{\text{GeV}}$ obtained by the STAR and PHENIX collaborations at RHIC are analyzed in the framework of $z$-scaling approach. The concept of the $z$-scaling is based on fundamental principles of self-similarity, locality, and fractality of hadron interactions at high energies. General properties of the data $z$-presentation are studied. Self-similarity of fractal structure of protons and fragmentation processes with strange particles is discussed. A microscopic scenario of constituent interactions developed within the $z$-scaling scheme is used to study the dependence of momentum fractions and recoil mass on the collision energy, transverse momentum and mass of produced inclusive particle, and to estimate the constituent energy loss. We consider that obtained results can be useful in study of strangeness origin, in searching for new physics with strange probes, and can serve for better understanding of fractality of hadron interactions at small scales.

We present new path integral studies on the Polyakov noncritical and Nambu–Goto critical string theories and their applications to $\mathrm{\text{QCD}}(SU(\infty ))$ interquark potential. We also evaluate the long distance asymptotic behavior of the interquark potential on the Nambu–Goto string theory with an extrinsic term in Polyakov’s string at $D\to \infty$. We also propose an alternative and a new view to covariant Polyakov’s string path integral with a fourth-order two-dimensional quantum gravity, is an effective stringy description for $\mathrm{\text{QCD}}(SU(\infty ))$ at the deep infrared region.

The elucidation of the nature of new phenomena requires a multi-pronged approach to understand the essential physics that underlies it. As an example, we study the simplified model containing a new scalar singlet accompanied by vector-like quarks. To be specific, we investigate three models with $SU{(2)}_L$-doublet, vector-like quarks with Yukawa couplings to a new scalar singlet and which also couple off-diagonally to corresponding Standard Model fermions of the first or third generation through the usual Higgs boson. We demonstrate that three classes of searches can play important and complementary roles in constraining this model. In particular, we find that missing energy searches designed for sparticle production, are also very sensitive to vector-like quarks.

In this work, we explicitly show resurgence relations between perturbative and one instanton sectors of the resonance energy levels for cubic and quartic anharmonic potentials in one-dimensional quantum mechanics. Both systems satisfy the Dunne–Ünsal relation and hence we are able to derive one-instanton nonperturbative contributions with the fluctuation terms to the energy merely from the perturbative data. We confirm our results with previous results obtained in the literature.

We analyze the inflationary scenario based on the tachyon field coupled with the radion of the second Randall–Sundrum model (RSII). The tachyon Lagrangian is derived from the dynamics of a 3-brane moving in the five-dimensional bulk. The AdS₅ geometry of the bulk is extended to include the radion. Using the Hamiltonian formalism we find four nonlinear field equations supplemented by the modified Friedmann equations of the RSII braneworld cosmology. After a suitable rescaling we reduce the parameters of our model to only one free parameter related to the brane tension and the AdS₅ curvature. We solve the equations numerically assuming a reasonably wide range of initial conditions determined by physical considerations. Varying the free parameter and initial conditions we confront our results with the Planck 2015 data.