Related papers: Solving the Hierarchy Problem Discretely

Exact discrete symmetries, if non-linearly realized, can reduce the ultraviolet sensitivity of a given theory. The scalars stemming from spontaneous symmetry breaking are massive without breaking the discrete symmetry, and those masses are…

We consider the simplest extension of the standard model, where torsion couples to spinor as well as to scalar fields, and in which the cosmological constant problem is solved.

Dynamical breaking of supersymmetry was long thought to be an exceptional phenomenon, but recent developments have altered this view. A question of great interest in the current framework is the value of the underlying scale of…

We show how to reduce the problem of solving members of a certain family of nonlinear differential equations to that of solving some corresponding linear differential equations.

Topological defects -- locations of local mismatch of order -- are a universal concept playing important roles in diverse systems studied in physics and beyond, including the universe, various condensed matter systems, and recently, even…

Collective phenomena in strongly nonequilibrium systems interacting with electromagnetic field are considered. Such systems are described by complicated nonlinear differential or integro-differential equations. The aim of this review is to…

In this paper we investigate an adaptive discretization strategy for ill-posed linear prob- lems combined with a regularization from a class of semiiterative methods. We show that such a discretization approach in combination with a…

Recently, a novel mechanism to address the hierarchy problem has been proposed \cite{Graham:2015cka}, where the hierarchy between weak scale physics and any putative `cutoff' $M$ is translated into a parametrically large field excursion for…

In this note we show that the cosmological domain wall and the de Sitter quantum breaking problems complement each other in theories with discrete symmetries that are spontaneously broken at low energies. Either the symmetry is exact and…

In this pedagogical paper we review the discrete symmetries of the Dirac equation using elementary tools, but in a comparative order: the usual 3 + 1 dimensional case and the 2 + 1 dimensional case. Motivated by new applications of the 2d…

We find a representation of smooth solutions to the Cauchy problem for a scalar multidimensional conservation law as small diffusion limit of a stochastic perturbation along characteristics. It helps, in particular, to study the process of…

We propose a model that provides a simultaneous solution to the doublet-triplet splitting problem of grand unified theories, the electroweak hierarchy problem and the strong CP problem. The mechanism is based on the dynamics of two…

We show that any second order linear ordinary diffrential equation with constant coefficients (including the damped and undumped harmonic oscillator equation) admits an exact discretization, i.e., there exists a difference equation whose…

Scale invariance may be a classical symmetry which is broken radiatively. This provides a simple way to stabilise the scale of electroweak symmetry breaking against radiative corrections. But for such a theory to be fully realistic, it must…

We present a new type of soliton solutions in nonlinear photonic systems with discrete point-symmetry. These solitons have their origin in a novel mechanism of breaking of discrete symmetry by the presence of nonlinearities. These so-called…

Symmetry is an important feature of many constraint programs. We show that any problem symmetry acting on a set of symmetry breaking constraints can be used to break symmetry. Different symmetries pick out different solutions in each…

We consider the Dirichlet problem for the nonlinear $p(x)$-Laplacian equation. For axially symmetric domains we prove that, under suitable assumptions, there exist Mountain-pass solutions which exhibit partial symmetry. Furthermore, we show…

The solution of the continuous time filtering problem can be represented as a ratio of two expectations of certain functionals of the signal process that are parametrized by the observation path. We introduce a new time discretisation of…

Discrete R symmetries are interesting from a variety of points of view. They raise the specter, however, of domain walls, which may be cosmologically problematic. In this note, we describe some of the issues. In many schemes for…

We study discrete R-symmetries, which appear in 4D low energy effective field theory derived from hetetoric orbifold models. We derive the R-symmetries directly from geometrical symmetries of orbifolds. In particular, we obtain the…