A conformally invariant generalization of string theory to higher-dimensional objects. Hierarchy of coupling constants

TL;DR

This paper introduces a conformally invariant model extending string theory to higher dimensions, with potential applications to cosmology and universe evolution, unifying string theory and gravity.

Contribution

It proposes a new conformally invariant sigma model for higher-dimensional objects, deriving its Hamiltonian formalism and exploring its cosmological implications.

Findings

Special cases recover string theory and Einstein gravity.

The model describes Friedmann-like cosmological models.

Universe evolution can be interpreted as evolution of 3D objects in higher-dimensional space.

Abstract

We suggest a conformally invariant generalization of string theory to higher-dimensional objects. As such a model, we consider a conformally invariant $\sigma$ model. For this theory, the Hamiltonian formalism is constructed, and the full set of constraints is found. The equations obtained are studied under a fixed gauge. It is shown that special cases of the model are string theory and Einstein's theory of gravity. Cosmological application of the suggested theory are studied. It is shown that Friedmann-like models can be described in this framework. Our models make it possible to interpret the Universe evolution as evolution of three-dimensional objects embedded in a higher-dimensional flat space-time.