Related papers: The ghost and weak dimensions of rings and ring sp…

Temporal ghost imaging is based on the temporal correlations of two optical beams and aims at forming a temporal image of a temporal object with a resolution, fundamentally limited by the photodetector resolution time and reaching 55 ps in…

We introduce the notion of a weakly reflective submanifold, which is an austere submanifold with a certain global condition, and study its fundamental properties. Using these, we determine weakly reflective orbits and austere orbits of…

We introduce the notion of negative topological dimension and the notion of weight for the asymptotic topological dimension. Quantizing of spaces of negative dimension is applied to linguistic statistics.

Aspects of duality and mirror symmetry in string theory are discussed. We emphasize, through examples, the importance of loop spaces for a deeper understanding of the geometrical origin of dualities in string theory. Moreover we show that…

We propose a framework in which Weinberg's anthropic explanation of the cosmological constant problem also solves the hierarchy problem. The weak scale is selected by chiral dynamics that controls the stabilization of an extra dimension.…

This paper introduces and studies a particular subclasses of the class of commutative rings with finite Gorenstein global (resp., weak) dimensions.

We propose a five-dimensional standard model which regards the Higgs field as a weak boson associated with the fifth dimension. The kinetic term of the Higgs field is obtained from the fifth components of field strengths defined in five…

In this paper, we introduce a new notion, called the integral dimension, for noetherian rings. It can be regarded as the weak Briancon-Skoda numbers of rings. The point is that every noetherian local ring has finite integral dimension.

We measure the spectral dimension of universes emerging from nonperturbative quantum gravity, defined through state sums of causal triangulated geometries. While four-dimensional on large scales, the quantum universe appears two-dimensional…

We define homological dimensions for S-algebras, the generalized rings that arise in algebraic topology. We compute the homological dimensions of a number of examples, and establish some basic properties. The most difficult computation is…

F-theory in its most general sense should be a theory defined on a worldvolume of higher dimension than the worldsheet, that reproduces string results perturbatively but includes nonperturbative supergravity solutions at the first-quantized…

We study the cosmology of bimetric theory with a composite matter coupling. We find two possible branches of background evolution. We investigate the question of stability of cosmological perturbations. For the tensor and vector…

We provide a short overview of recent progress made in our understanding of the dark sector based on the Swampland program which in turn is rooted in lessons from string theory. We explain how the existence of one extra mesoscopic dimension…

Ghost tomography using single-pixel detection extends the emerging field of ghost imaging to three dimensions, with the use of penetrating radiation. In this work, a series of spatially random x-ray intensity patterns is used to illuminate…

Very recently, it was pointed out that when basic ideas of the Swampland program are combined with the cosmological hierarchy problem (i.e. the smallness of the dark energy in Planck units) and together are confronted to experiment lead to…

We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several…

The "Auxiliary Extra Dimension" model was proposed in order to provide a geometrical interpretation to modifications of general relativity, in particular to non-linear massive gravity. In this context, the theory was shown to be ghost free…

A hidden sector that kinetically mixes with the Minimal Supersymmetric Standard Model provides simple and well-motivated dark matter candidates that possess many of the properties of a traditional weakly interacting massive particle (WIMP).…

We consider the set of all the ideals of a ring, endowed with the coarse lower topology. The aim of this paper is to study the topological properties of distinguished subspaces of this space and detect the spectrality of some of them.

Assessing the presence of chemical, biological, radiological and nuclear threats is a crucial task which is usually dealt with by analyzing the presence of spectral features in a measured absorption profile. The use of quantum light allows…