On The Equivalence Of Four Dimensional And Two dimensional Field Theories

TL;DR

This paper demonstrates that four-dimensional Einstein and Yang-Mills theories can be constructed from two-dimensional quantities, revealing an inherent equivalence to related two-dimensional field theories.

Contribution

It establishes a novel equivalence between four-dimensional and two-dimensional field theories based on their structural and topological properties.

Findings

Four-dimensional theories possess a distinguished two-dimensional substructure.

Four-dimensional Einstein and Yang-Mills theories are equivalent to related two-dimensional theories.

Theories are constructed from two-dimensional quantities, highlighting a fundamental dimensional reduction.

Abstract

We investigate the dimensional, the dynamical and the topological structures of four dimensional Einstein and Yang-Mills theories. It is shown that these theories are constructed from two dimensional quantities, so that they possess always a distinguished two dimensional substructure. In this sense the four dimensional field theories are equivalent to related two dimensional field theories.