Torsion, Dilaton and Gauge Couplings

TL;DR

This paper explores how torsion can couple to gauge fields via scalar fields in the early universe, leading to a scenario where gauge couplings evolve and torsion diminishes, aligning with Einstein's theory at later times.

Contribution

It proposes a model where torsion couples to gauge fields through scalar fields, explaining the evolution of gauge couplings and torsion in the early universe within a string theory landscape context.

Findings

Torsion couples to gauge fields via scalar fields in the early universe.

Gauge couplings evolve with scalar fields and become constant as torsion vanishes.

The universe transitions from a Riemann-Cartan to a Riemannian geometry, recovering Einstein's theory.

Abstract

Non-Abelian gauge fields are traditionally not coupled to torsion due to violation of gauge invariance. However, it is possible to couple torsion to Yang-Mills fields while maintaining gauge invariance provided one accepts that the gauge couplings then become scalar fields. In the past this has been untenable from experimental constraints at the current epoch for the electromagnetic field at least. Recent researches on the "landscape" arising out of string theory provides for many scalar fields which eventually determine the various low energy parameters including gauge couplings in the universe. With this scenario, we argue that the very early universe provides a Riemann-Cartan geometry with non-zero torsion coupling to gauge fields. The torsion is just the derivative of gauge coupling (scalar) fields. As a result, in the evolution of the Universe, when the scalar (moduli) fields determine the geometry of the universe to be Riemannian, torsion goes to zero, implying that the associated modulus (and hence the gauge coupling) has a constant value. An equivalent view is that the modulus fixes the gauge coupling at some constant value causing the torsion to vanish as a consequence. Of course, when torsion vanishes we recover Einstein's theory for further evolution of the universe.