Related papers: Planar Super-Landau Models
In this paper we study ground-states of the fractional Gierer-Meinhardt system on the line, namely the solutions of the problem \begin{equation*} \left\{\begin{array}{ll} (-\Delta)^su+u-\frac{u^2}{v}=0,\quad &\mathrm{in}~\mathbb{R},\\…
Landau quantization of low-energy quasiparticles (QPs) in the mixed state of gapless superconductors is a celebrated problem. So far, the only superconducting system that has been shown to host Landau levels (LLs) of Bogoliubov QPs is the…
We study the Landau-problem on the $\theta$-deformed two-torus and use well-known projective modules to obtain perturbed spectra. For a strong magnetic field B the problem can be restricted to one particular Landau-level. First we represent…
The minimal dark matter model is given a supersymmetric extension. A super SU(2)L quintuplet is introduced with its fermionic neutral component still being the dark matter, the dark matter particle mass is about 19.7 GeV. Mass splitting…
At even-denominator Landau level filling fractions, such as $\nu=1/2$, the ground state, in most cases, has no energy gap, and there is no quantized plateau in the Hall conductance. Nevertheless, the states exhibit non-trivial low-energy…
A general strategy is proposed to explore the low-energy properties of two-dimensional nonlinear $\sigma$ models with $\theta$ terms. We demonstrate its application to nonlinear $\sigma$ models with the target space $\text{SU($N$)}$/H,…
In this paper we present a solution to the $\mu$ problem in an SO(10) supersymmetric grand unified model with gauge mediated and D-term supersymmetry breaking. A Peccei-Quinn symmetry is broken at the messenger scale $M\sim 10^{12}$ GeV and…
We consider firstly simple D=4 superalgebra with six real tensorial central charges $Z_{\mu\nu}$, and discuss its possible realizations in massive and massless cases. Massless case is dynamically realized by generalized Ferber-Shirafuji…
The (4,0) supermultiplet in 6 dimensions contains a 4th rank tensor gauge field with the symmetries of the Riemann tensor and is superconformal, with 32+32 supersymmetries. Dimensional reduction on a circle gives the 5D N=8 supergravity…
We generalize previous results for the superplane Landau model to exhibit an explicit worldline N = 2 supersymmetry for an arbitrary magnetic field on any two-dimensional manifold. Starting from an off-shell N = 2 superfield formalism, we…
We consider an isotropic two dimensional harmonic oscillator with arbitrarily time-dependent mass $M(t)$ and frequency $\Omega(t)$ in an arbitrarily time-dependent magnetic field $B(t)$. We determine two commuting invariant observables (in…
We propose a simple mechanism for solving the $\mu$ problem in the context of minimal low--energy supergravity models. This is based on the appearance of non--renormalizable couplings in the superpotential. In particular, if $H_1H_2$ is an…
The general theory of N = 1 supergravity with supermatter is studied using a canonical approach. The supersymmetry and gauge constraint generators are found. The framework is applied to the study of a Friedmann minisuperspace model. We…
We find the general conditions for viable cosmological solution at the background level in bigravity models. Furthermore, we constrain the parameters by comparing to the Union 2.1 supernovae catalog and identify, in some cases analytically,…
We introduce a variant of dipole representation for composite fermions in a half-filled Landau level, taking into account the symmetry under exchange of particles and holes. This is implemented by a special constraint on composite fermion…
We show that if $M$ is an Einstein hypersurface in an irreducible Riemannian symmetric space $\overline{M}$ of rank greater than $1$ (the classification in the rank-one case was previously known), then either $\overline{M}$ is of noncompact…
We consider an entire graph $S$ in $\mathbb R^{N+1}$ of a continuous real function $f$ over $\mathbb R^{N}$ with $N\ge 1$. Let $\Omega$ be an unbounded domain in $\mathbb R^{N+1}$ with boundary $S$. Consider nonlinear diffusion equations of…
The Milnor number of an isolated hypersurface singularity, defined as the codimension $\mu(f)$ of the ideal generated by the partial derivatives of a power series $f$ that represents locally the hypersurface, is an important topological…
The minimal supersymmetric standard model with soft breaking has a large landscape of supersymmetric particle mass hierarchies. This number is reduced significantly in well-motivated scenarios such as minimal supergravity and alternatives.…
Let $(M,g)$ be a $m$-dimensional compact Riemannian manifold without boundary. Assume $\kappa\in C^2(M)$ is such that $-\Delta_g+\kappa$ is coercive. We prove the existence of a solution to the supercritical problems $$ -\Delta_gu+\kappa u=…