Kaluza–Klein theory without extra dimensions: curved Clifford space

Kaluza-Klein Theory without Extra Dimensions: Curved Clifford Space‡

A theory in which 16-dimensional curved Clifford space (C-space) provides a realization of Kaluza-Klein theory is investigated. No extra dimensions of spacetime are needed: “extra dimensions” are in C-space. It is shown that the covariant Dirac equation in C-space contains Yang-Mills fields of the U(1)× SU(2)×SU(3) group as parts of the generalized spin connection of the C-space.

A Superstring Theory in Four Curved Space-time Dimensions *

Neveu-Schwarz-Ramond type heterotic and type-II superstrings in four dimensional curved space-time are constructed as exact N = 1 superconformal theories. The tachyon is eliminated with a GSO projection. The theory is based on the N=1 superconformal gauged WZW model for the anti-de Sitter coset SO(3, 2)/SO(3, 1) with integer central extension k = 5. The model has dynamical duality properties in...

Extra Dimensions in Superstring Theory

Dimensional Reduction without Continuous Extra Dimensions

We describe a novel approach to dimensional reduction in classical field theory. Inspired by ideas from noncommutative geometry, we introduce extended algebras of differential forms over spacetime, generalized exterior derivatives, and generalized connections associated with the “geometry” of space-times with discrete extra dimensions. We apply our formalism to theories of gaugeand gravitationa...

Motivations for Searching for Extra Space Dimensions

On behalf on the ATLAS and CMS collaborations The introduction of extra space dimensions in the theory could be an elegant way to solve the hierarchy problem. There could even be one energy scale at which all interactions could unify. The limits coming from our knowledge of the gravitation at low distance allow this energy scale to be as low as few TeV. This situation is extremely interesting e...