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The Virasoro minimal models with boundary are described in the Landau-Ginzburg theory by introducing a boundary potential, function of the boundary field value. The ground state field configurations become non-trivial and are found to obey…
A search for the supersymmetric partners of the Standard Model bottom and top quarks is presented. The search uses 36.1 fb$^{-1}$ of $pp$ collision data at $\sqrt{s}=13$ TeV collected by the ATLAS experiment at the Large Hadron Collider.…
The present experimental and theoretical knowledge of the physics of electroweak symmetry breaking is reviewed. Data still favor a light Higgs boson, of a kind that can be comfortably accommodated in the Standard Model or in its Minimal…
In this manuscript, I briefly review the Benchmark Planes in the Two-Real-Singlet Model (TRSM), a model that enhances the Standard Model (SM) scalar sector by two real singlets that obey a Z2 x Z2' symmetry. In this model, all fields…
The hexagon is the least-perimeter tile in the Euclidean plane for any given area. On hyperbolic surfaces, this "isoperimetric" problem differs for every given area, as solutions do not scale. Cox conjectured that a regular $k$-gonal tile…
The exact matching condition is given for hadron matrix elements calculated in any two different schemes, in particular, in the lattice and dimensional regularization, (modified) minimal subtraction $\overline{\rm MS}$ schemes. The result…
For a three dimensional system we answer two questions, how simple a particle system might be to show the quasicrystal order and, what system features are the most important for quasicrystal formation? One-component system of particles with…
We present a brief history of quasicrystals and a short introduction to classical lattice-gas models of interacting particles. We discuss stability of non-periodic tilings and one-dimensional sequences of symbols seen as ground states of…
A simple solvable toy model exhibiting effective restoration of chiral symmetry in excited hadrons is constructed. A salient feature is that while physics of the low-lying states is crucially determined by the spontaneous breaking of chiral…
We present evidence for a novel finite-temperature phase transition in the phason elasticity of quasicrystals. A tiling model for energetically stabilized decagonal quasicrystals has been studied in an extensive series of Monte Carlo…
We prove that if an N-vortex pair nearly minimizes the Yang-Mills-Higgs energy, then it is second order close to a minimizer. First we use new weighted inequalities in two dimensions and compactness arguments to show stability for sections…
Possible realistic scenarios are investigated in the minimal supersymmetric standard model (MSSM) Higgs sector extended by dimension-six effective operators. The CP-odd Higgs boson with low mass around 30--90 GeV could be consistently…
We present an ultraviolet extension of the Twin Higgs in which the radial mode of twin symmetry breaking is itself a pseudo-goldstone boson. This "turtle" structure raises the scale of new colored particles in exchange for additional states…
There could be another scalar in nature quasi-degenerate with the observed one (h125). This is possible in models such as the Next-to-Minimal Supersymmetric Standard Model (NMSSM). The scenario(s) with a single Higgs boson can be compared…
In the light of the recent Lin, Lunin, Maldacena (LLM) results we investigate 1/2-BPS geometries in minimal (and next-to minimal) supergravity in D=6 dimensions. In the case of minimal supergravity, solutions are given by fibrations of a…
Quasiparticle states near the surface of a quasi-one-dimensional organic superconductor $({TMTSF})_{2}{PF}_6$ are studied based on an extended Hubbard model on a quasi-one dimensional lattice at quarter-filling. Three types of pairing…
For the general two-Higgs doublet model with Yukawa sector of type II (type II 2HDM), the Higgs alignment limit conditions are obtained for the neutral Higgs bosons with indefinite CP-parity $h_1, h_2$ or $h_3$, based on the symbolic…
Ground-state properties of the two-dimensional $S=1/2$ random Heisenberg models are investigated by the exact-diagonalization method. The phase diagram of the bond-random model (the $\pm J$ model) is the same as that of the corresponding…
If the Higgs boson has a composite nature, it might be the 4-dimensional hologram of a gauge field living in a warped extra dimension. In this talk I discuss a minimal, calculable model that passes all electroweak precision tests, included…
We consider a two-dimensional lattice model of equilibrium statistical mechanics, using nearest neighbor interactions based on the matching conditions for an aperiodic set of 16 Wang tiles. This model has uncountably many ground state…