Related papers: Shape of Deconstruction
We construct two classes of exact solutions to six and higher dimensional Einstein-Maxwell theory in which the metric functions can be written as convolution-like integrals of two special functions. The solutions are regular everywhere and…
Let X be a smooth projective variety with the action of the n dimensional torus. The article describes the moduli space of torus equivariant morphisms from stable toric varieties into X as the inverse limit of the GIT quotients of X and…
We build a toy model of differential geometry on the real line, which includes derivatives of the second order. Such construction is possible only within the framework of noncommutative geometry. We introduce the metric and briefly discuss…
A value of the cosmological constant in a toy model of the five-dimensional universe is calculated in such a manner that it remains in agreement with both astronomical observations and the quantum field theory concerning the zero-point…
It has long been understood that certain theories of ghost free massive gravity and their multi-graviton extensions can be thought of as arising from a higher dimensional theory of gravity, upon discretising the extra dimension. However,…
The dynamics of Maxwell-dilaton theory in Minkowski spacetime are studied using fully nonlinear, numerical evolutions. This model represents the flat-space sector of Einstein-Maxwell-Dilaton theory which has attracted interest recently…
We study the implication of the distance and the cobordism conjecture on the 6-dimensional Einstein-Maxwell theory compactified on $S^2$. In this toy model, the radion potential is stabilized by the conspiracy of the curvature of $S^2$ and…
We construct gauge theories in two extra dimensions compactified on the chiral square, which is a simple compactification that leads to chiral fermions in four dimensions. Stationarity of the action on the boundary specifies the boundary…
Spatial compactification on $\mathbb R^{3} \times \mathbb S^1_L$ at small $\mathbb S^1$-size $L$ often leads to a calculable vacuum structure, where various "topological molecules" are responsible for confinement and the realization of the…
The development of a nonlinear structural theory (model) for isotropic linear-elastic finite continua is the main objective of the study. To derive the theory, we used Taylor's multivariable expansion and Bubnov-Galerkin's weak formulation.…
We study sets and groups definable in tame expansions of o-minimal structures. Let $\mathcal {\widetilde M}= \langle \mathcal M, P\rangle$ be an expansion of an o-minimal $\mathcal L$-structure $\cal M$ by a dense set $P$, such that three…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
If a theory has more than one classically stable vacuum, quantum tunneling and thermal jumps make the transition between the vacua possible. The transition happens through a first order phase transition started by nucleation of a bubble of…
A unified theory of material defects, incorporating both the smooth and the singular descriptions, is presented based upon the theory of currents of Georges de Rham. The fundamental geometric entity of discourse is assumed to be represented…
We provide an explicit construction of a manifestly duality invariant, interacting deformation of Maxwell theory in four dimensions in terms of mutually local, but interacting 1- and 3-forms. Interestingly, our theory is formulated directly…
Building on work of Kapouleas and Yang, we construct sequences of minimal surfaces embedded in the round 3-sphere which converge to the Clifford torus counted with multiplicity two and have second fundamental form blowing up at every point…
A construction of conservation laws for chiral models (generalized sigma-models on a two-dimensional space-time continuum using differential forms is extended in such a way that it also comprises corresponding discrete versions. This is…
The Distance Conjecture states that an infinite tower of modes becomes exponentially light when approaching an infinite distance point in field space. We argue that the inherent path-dependence of this statement can be addressed when…
We study the Matrix theory description of M-theory compactified on $T^4$ and $T^5$. M-theory on $T^4$ is described by the six dimensional (2,0) fixed point field theory compactified on a five torus, $\widetilde T^5$. For M-theory on $T^5$…
Starting from the hypothesis that both physics, in particular space-time and the physical vacuum, and the corresponding mathematics are discrete on the Planck scale we develop a certain framework in form of a '{\it cellular network}'…