International Journal of Modern Physics A

In the present paper we argue that the correction to the Higgs mass coming from the bound state of 6 top and 6 antitop quarks, predicted early by Froggatt and ourselves, leads to the Standard Model vacuum stability and confirms the accuracy of the multiple point principle (principle of degenerate vacua) for all experimentally valued parameters (Higgs mass, top-quark mass, etc.). Fitting to get the vacuum degeneracy requires a mass of the bound state, just in the region of the new two photon state in Large Hadron Collider, 750–760 GeV.

We study the Renormalization Group (RG) flow of AC conductivity in soft wall model of holographic QCD. We consider the charged black hole metric and the explicit form of AC conductivity is obtained at the cutoff surface. We plot the numerical solution of conductivity flow as a function of radial coordinate. The equation of gauge field is also considered and the numerical solution is obtained for AC conductivity as a function of frequency. The results for AC conductivity are also obtained for different values of chemical potential and Gauss–Bonnet couplings.

We develop the spectral representation of propagator for $n$ mixing fermion fields in the case of $P$-parity violation. The approach based on the eigenvalue problem for inverse matrix propagator makes possible to build the system of orthogonal projectors and to represent the matrix propagator as a sum of poles with positive and negative energies. The procedure of multiplicative renormalization in terms of spectral representation is investigated and the renormalization matrices are obtained in a closed form without the use of perturbation theory. Since in theory with $P$-parity violation the standard spin projectors do not commute with the dressed propagator, they should be modified. The developed approach allows us to build the modified (dressed) spin projectors for a single fermion and for a system of fermions.

We construct models where initial and boundary conditions can be found from the fundamental rules of physics, without the need to assume them, they will be derived from the action principle. Those constraints are established from physical viewpoint, and it is not in the form of Lagrange multipliers. We show some examples from the past and some new examples that can be useful, where constraint can be obtained from the action principle. Those actions represent physical models. We show that it is possible to use our rule to get those constraints directly.

String theory proves to be an imperative tool to explore the critical behavior of the quantum dissipative system. We discuss the quantum particles moving in two dimensions, in the presence of a uniform magnetic field, subject to a periodic potential and a dissipative force, which are described by the dissipative Wannier–Azbel–Hofstadter (DWAH) model. Using string theory formulation of the model, we find that the elementary excitations of the system at the generic points of the off-critical regions, in the zero temperature limit are quons, which satisfy $q$-deformed statistics.

We analyze the compatibility of the recent LHC signals and the TeV-scale left–right model(s) in the minimal nonsupersymmetric SO(10) framework. We show that the models in which the Higgs content is selected based on the extended survival hypothesis do not allow the $W_R$ boson to be at the TeV-scale. By relaxing this conjecture, we investigate various scenarios where a number of colored-scalars, originated from various Pati–Salam multiplets, are light and whence they survive down to the low energies. Performing a detailed renormalization group analysis with various low-energy Higgs configurations and symmetry breaking chains, while keeping the high energy Higgs content unmodified; we find that, among a number of possibilities, the models which have a light color-triplet scalar, and its combination with a light color-sextet, particularly stand out. Although these models do allow a TeV-scale $W_R$ boson, generating the required value of the gauge coupling $g_R$ at this scale is nontrivial.

We analyze the interplay between gauge fixing and boundary conditions in two-dimensional U(1) lattice gauge theory. We show on the basis of a general argument that periodic boundary conditions result in an ill-defined weak coupling approximation but that the approximation can be made well-defined if the boundaries are fixed to zero. We confirm this result in the particular case of the Feynman gauge. We show that the zero momentum mode divergence in the propagator that appears in the Feynman gauge vanishes when the weak coupling approximation is well-defined. In addition we obtain exact results (for arbitrary coupling), including finite size corrections, for the partition function and for general one-point and two-point functions in the axial gauge under both periodic and zero boundary conditions and confirm these results numerically. The dependence of these objects on both lattice size and coupling constant is investigated using specific examples. These exact results may provide insight into similar gauge fixing issues in more complex models.

A toy-model with $SU{(2)}_{\mathrm{\text{TC}}}$ dynamics confined at high scales ${\mathrm{\Lambda }}_{\mathrm{\text{TC}}}\gg 100\mathrm{\text{GeV}}$ enables to construct Dirac UV completion from the original chiral multiplets predicting a vector-like nature of their weak interactions consistent with electroweak precision tests. In this work, we investigate a potential of the lightest scalar baryon-like (T-baryon) state $B^0=UD$ with mass $m_B\gtrsim 1\mathrm{\text{TeV}}$ predicted by the simplest two-flavor vector-like confinement model as a dark matter (DM) candidate. We show that two different scenarios with the T-baryon relic abundance formation before and after the electroweak (EW) phase transition epoch lead to symmetric (or mixed) and asymmetric DM, respectively. Such a DM candidate evades existing direct DM detection constraints since its vector coupling to $Z$ boson absents at tree level, while one-loop gauge boson mediated contribution is shown to be vanishingly small close to the threshold. The dominating spin-independent (SI) T-baryon–nucleon scattering goes via tree-level Higgs boson exchange in the $t$-channel. The corresponding bound on the effective T-baryon–Higgs coupling has been extracted from the recent LUX data and turns out to be consistent with naive expectations from the light technipion case $m_{\tilde{\pi }}\ll {\mathrm{\Lambda }}_{\mathrm{\text{TC}}}$. The latter provides the most stringent phenomenological constraint on strongly-coupled $SU{(2)}_{\mathrm{\text{TC}}}$ dynamics so far. Future prospects for direct and indirect scalar T-baryon DM searches in astrophysics as well as in collider measurements have been discussed.