Axion and dilaton + metric emerge from local and linear electrodynamics

TL;DR

This paper explores how axion, dilaton, and metric fields naturally emerge from a purely premetric, linear electrodynamics framework, linking spacetime structure to electromagnetic response without presupposing a metric.

Contribution

It demonstrates that the metric, axion, and dilaton fields can be derived solely from electromagnetic response tensors, unifying spacetime geometry with electrodynamics.

Findings

Birefringence-free conditions lead to metric, axion, and dilaton emergence.

The metric can be derived from electromagnetic response properties.

Recovery of Riemannian spacetime when axion vanishes and dilaton is constant.

Abstract

We take a quick look at the different possible universally coupled scalar fields in nature. Then, we discuss how the gauging of the group of scale transformations (dilations), together with the Poincare group, leads to a Weyl-Cartan spacetime structure. There the dilaton field finds a natural surrounding. Moreover, we describe shortly the phenomenology of the hypothetical axion field. --- In the second part of our essay, we consider a spacetime, the structure of which is exclusively specified by the premetric Maxwell equations and a fourth rank electromagnetic response tensor density $\chi^{ijkl}= -\chi^{jikl}= -\chi^{ijlk}$ with 36 independent components. This tensor density incorporates the permittivities, permeabilities, and the magneto-electric moduli of spacetime. No metric, no connection, no further property is prescribed. If we forbid birefringence (double-refraction) in this model of spacetime, we eventually end up with the fields of an axion, a dilaton, and the 10 components of a metric tensor with Lorentz signature. If the dilaton becomes a constant (the vacuum admittance) and the axion field vanishes, we recover the Riemannian spacetime of general relativity theory. Thus, the metric is encapsulated in $\chi^{ijkl}$, it can be derived from it. [file CarlBrans80_07.tex]