Abstract

Requiring that 4-rank “electromagnetic” gauge field strength, in four time and four space dimensions ((4+4)-dimensions), satisfies the Grassmann-Pl¨ucker relations, it is shown that by choosing appropriate ansatz (for a basic basis) one can derive two dual strings: One string associated with a (1 + 3)-world, and the other with a (3 + 1)-world. An interesting aspect of this mechanism is that the string in the (1 + 3)-world turns out to be dual to the string in the (3 + 1)-world. It may helpful to clarify the main achievement of this work for a possible non-specialist reader. The central idea is to show that the complete description of our universe in (1 + 3)-dimensions (one time and three space dimensions) may require to assume a mirror dual universe in (3 + 1)-dimensions. So, if an object (3-brane) ‘lives’ in higher dimensional-world that include both the (1 + 3)-world and the mirror (3 + 1)-world, such as the (4 + 4)-dimensional-world, one may be able to show that can be broken into two simpler objects (strings or 1-branes). The key point our achievement is that the hidden symmetry relating these two simpler objects is duality.

This work is licensed under a Creative Commons Attribution 4.0 License.