International Journal of Modern Physics A

Four-dimensional compactifications of string theory provide a controlled set of possible gauge representations accounting for BSM particles and dark sector components. In this review, constraints from perturbative Type II string compactifications in the geometric regime are discussed in detail and then compared to results from heterotic string compactifications and nonperturbative/nongeometric corners. As a prominent example, an open string realization of the QCD axion is presented. The status of deriving the associated low-energy effective action in four dimensions is discussed and open avenues of major phenomenological importance are highlighted. As examples, a mechanism of closed string moduli stabilization by D-brane backreaction as well as one-loop threshold corrections to the gauge couplings and balancing a low string scale $M_{\mathrm{\text{string}}}$ with unisotropic compact dimensions are discussed together with implications on potential future new physics observations. For illustrative purposes, an explicit example of a globally consistent D6-brane model with MSSM-like spectrum on $T^6/({\mathbb{Z}}_2\times {\mathbb{Z}}_6\times \mathrm{\Omega }{ℛ})$ is presented.

In this review, we present a theory of cosmological constant and dark energy (DE), based on the topological structure of the vacuum. The multiple point principle (MPP) is reviewed. It demonstrates the existence of the two vacua into the SM. The Froggatt–Nielsen’s prediction of the top-quark and Higgs masses is given in the assumption that there exist two degenerate vacua in the SM. This prediction was improved by the next-order calculations. We also considered Sidharth’s theory of cosmological constant based on the noncommutative geometry of the Planck scale space–time, what gives an extremely small DE density providing the accelerating expansion of the Universe. Theory of two degenerate vacua — the Planck scale phase and electroweak (EW) phase — is also reviewed, topological defects in these vacua are investigated, also the Compton wavelength phase suggested by Sidharth is discussed. A general theory of the phase transition and the problem of the vacuum stability in the SM is reviewed. Assuming the existence of a new scalar $S$ bound state $6t+6\bar{t}$, earlier predicted by Froggatt, Nielsen and Laperashvili, we try to provide the vacuum stability in the SM and exact accuracy of the MPP.

This is a review of some recent works which demonstrate how the classical equations of gravity in AdS themselves hold the key to understand their holographic origin in the form of a strongly coupled large N QFT whose algebra of local operators can be generated by a few (single-trace) elements. I discuss how this can be realized by reformulating Einstein’s equations in AdS in the form of a nonperturbative RG flow that further leads to a new approach toward constructing strongly interacting QFTs. In particular, the RG flow can self-determine the UV data that are otherwise obtained by solving classical gravity equations and demanding that the solutions do not have naked singularities. For a concrete demonstration, I focus on the hydrodynamic limit in which case this RG flow connects the AdS/CFT correspondence with the membrane paradigm, and also reproduces the known values of the dual QFT transport coefficients.

We exploit the techniques of Bonora–Tonin superfield formalism to derive the off-shell nilpotent and absolutely anticommuting (anti-)BRST as well as (anti-)co-BRST symmetry transformations for the (1+1)-dimensional (2D) bosonized vector Schwinger model. In the derivation of above symmetries, we invoke the (dual)-horizontality conditions as well as gauge and (anti-)co-BRST invariant restrictions on the superfields that are defined onto the (2,2)-dimensional supermanifold. We provide geometrical interpretation of the above nilpotent symmetries (and their corresponding charges). We also express the nilpotency and absolute anticommutativity of the (anti-)BRST and (anti-)co-BRST charges within the framework of augmented superfield formalism.

In mean field approximation, the grand canonical potential of SU(3) Polyakov linear-$\sigma$ model (PLSM) is analyzed for chiral phase transition, ${\sigma }_l$ and ${\sigma }_s$ and for deconfinement order-parameters, $\varphi$ and ${\varphi }^{\ast }$ of light- and strange-quarks, respectively. Various PLSM parameters are determined from the assumption of global minimization of the real part of the potential. Then, we have calculated the subtracted condensates $({\mathrm{\Delta }}_{l,s})$. All these results are compared with recent lattice QCD simulations. Accordingly, essential PLSM parameters are determined. The modeling of the relaxation time is utilized in estimating the conductivity properties of the QCD matter in thermal medium, namely electric $[{\sigma }_{\mathrm{\text{el}}}(T)]$ and heat $[\kappa (T)]$ conductivities. We found that the PLSM results on the electric conductivity and on the specific heat agree well with the available lattice QCD calculations. Also, we have calculated bulk and shear viscosities normalized to the thermal entropy, $\xi /s$ and $\eta /s$, respectively, and compared them with recent lattice QCD. Predictions for $(\xi /s)/({\sigma }_{\mathrm{\text{el}}}/T)$ and $(\eta /s)/({\sigma }_{\mathrm{\text{el}}}/T)$ are introduced. We conclude that our results on various transport properties show some essential ingredients, that these properties likely come up with, in studying QCD matter in thermal and dense medium.

Sometime back, a self-similarity based model of the proton structure function at small $x$ was proposed by Lastovicka. We make reanalysis of this model with most recent HERA data. No significance difference with the earlier analysis is found. Both the analyses have singularity within the kinematical range of $x$: $0\le x\le 1$. We therefore study the model with the additional assumption that it should be singularity free, imposing positivity conditions on the model parameters. This results in a new model which is, however, phenomenologically valid only in a limited low $Q^2$ range. We therefore make further generalization of the defining self-similar unintegrated Parton Density Function (uPDF) and show that the with proper generalizations and initial conditions on them not only remove the undesired singularity but also results in a structure function with logarithmic growth in $Q^2$ closer to QCD. The phenomenological range of validity is then found to be much larger than the earlier versions. We also extrapolate the models to large $x$ in a parameter-free way. The possibility of incorporation of Transverse Momentum Dependent (TMD) PDF in this approach is explored as well.

The problem of the gauge hierarchy is brought up in a hypercomplex scheme for a $U(1)$ field theory; in such a scheme, a compact gauge group is deformed through a $\gamma$-parameter that varies along a noncompact internal direction, transverse to the $U(1)$ compact one, and thus an additional $SO(1,1)$ gauge symmetry is incorporated. This transverse direction can be understood as an extra internal dimension, which will control the spontaneous symmetry breakdown, and will allow us to establish a mass hierarchy. In this mechanism, there is no brane separation to be estabilized as in the braneworld paradigm, however, a different kind of fine-tuning is needed in order to generate the wished electroweak/Planck hierarchy. By analyzing the effective self-interactions and mass terms of the theory, an interesting duality is revealed between the real and hybrid parts of the effective potential. This duality relates the weak and strong self-interaction regimes of the theory, due to the fact that both mass terms and self-coupling constants appear as one-parameter flows in $\gamma$. Additionally, the $\gamma$-deformation will establish a flow for the electromagnetic coupling that mimics the renormalization group flow for the charge in QED.

We study a $U(1)\times U(1)$ gauge theory discussing its vortex solutions and supersymmetric extension. In our set-up, the dynamics of one of two Abelian gauge fields is governed by a Maxwell term, the other by a Chern–Simons term. The two sectors interact via a BF gauge field mixing and a Higgs portal term that connects the two complex scalars. We also consider the supersymmetric version of this system which allows to find for the bosonic sector BPS equations in which an additional real scalar field enters into play. We study numerically the field equations finding vortex solutions with both magnetic flux and electric charge.

We present a mathematically rigorous quantum-mechanical treatment of a two-dimensional nonrelativistic quantum dual theories (with oscillator- and Coulomb-like potentials) on pseudosphere. We construct all self-adjoint Schrödinger operators for these theories and present solutions of the corresponding spectral problems. We show, that there is one-to-one correspondence between spectral points of the energy-coupling constant planes not only for discrete, but also for continuous spectra and corresponding eigenfunctions forming the complete orthonormalized systems.

We show that it is possible to construct observables to test the existence of new physics in a model independent way for the $D^0\to VV$ modes using a time-dependent analysis of the neutral $D$ meson. We show that it is possible to identify whether the NP is due to decay, mixing or a combination of both. We also provide numerical estimates for the polarization amplitudes for the $D^0\to \overline{K^{\ast 0}}{\rho }^0$ mode and show that our analysis is consistent with the present data.

We present generalized evolution equations and factorization in terms of the truncated Mellin moments (TMM) of the parton distributions and structure functions. We illustrate the x and Q² dependence of TMM in the polarized case. Using the TMM approach we compare the integrals of g₁ with HERMES and COMPASS data from the limited x-ranges.

In this paper, the existence of the Weyl representation for the canonical commutation relations algebras was proved in a Krein space.

Complete set of cylindrical modes is constructed for the electromagnetic field inside and outside a cylindrical shell in the background of $(D+1)$-dimensional dS space–time. On the shell, the field obeys the generalized perfect conductor boundary condition. For the Bunch–Davies vacuum state, we evaluate the vacuum expectation values (VEVs) of the electric field squared and of the energy–momentum tensor. The shell-induced contributions are explicitly extracted. In this way, for points away from the shell, the renormalization is reduced to the one for the VEVs in the boundary-free dS bulk. As a special case, the VEVs are obtained for a cylindrical shell in the $(D+1)$-dimensional Minkowski bulk. We show that the shell-induced contribution in the electric field squared is positive for both the interior and exterior regions. The corresponding Casimir–Polder forces are directed toward the shell. The vacuum energy–momentum tensor, in addition to the diagonal components, has a nonzero off-diagonal component corresponding to the energy flux along the direction normal to the shell. This flux is directed from the shell in both the exterior and interior regions. For points near the shell, the leading terms in the asymptotic expansions for the electric field squared and diagonal components of the energy–momentum tensor are obtained from the corresponding expressions in the Minkowski bulk replacing the distance from the shell by the proper distance in the dS bulk. The influence of the gravitational field on the local characteristics of the vacuum is essential at distances from the shell larger than the dS curvature radius. The results are extended for confining boundary conditions of flux tube models in QCD.