The String Dilaton and a Least Coupling Principle

TL;DR

The paper investigates whether a massless dilaton, predicted by string theory, can be reconciled with stringent experimental tests. It proposes a Least Coupling Principle: nonperturbative string-loop effects can yield universal, multiplicative dilaton couplings, causing cosmological evolution to drive the dilaton toward an extremum of the common coupling function $B(\varphi)$ and thereby decouple from matter. Through radiation- and matter-dominated epochs, including mass-threshold and phase-transition effects, the authors derive analytical and semi-analytical results showing that the present dilaton coupling is highly suppressed, predicting tiny residual violations of the equivalence principle and slow variations of fundamental constants. The work highlights equivalence-principle tests as sensitive probes of string-scale physics and proposes a criterion for selecting string models that naturally suppress observable dilaton effects.

Abstract

It is pointed out that string-loop modifications of the low-energy matter couplings of the dilaton may provide a mechanism for fixing the vacuum expectation value of a massless dilaton in a way which is naturally compatible with existing experimental data. Under a certain assumption of universality of the dilaton coupling functions , the cosmological evolution of the graviton-dilaton-matter system is shown to drive the dilaton towards values where it decouples from matter (``Least Coupling Principle"). Quantitative estimates are given of the residual strength, at the present cosmological epoch, of the coupling to matter of the dilaton. The existence of a weakly coupled massless dilaton entails a large spectrum of small, but non-zero, observable deviations from general relativity. In particular, our results provide a new motivation for trying to improve by several orders of magnitude the various experimental tests of Einstein's Equivalence Principle (universality of free fall, constancy of the constants,\dots).

Figures (3)

• Figure 1: The factor by which $\varphi$ is attracted (when the early universe cools down through $T \sim m_A$) toward a minimum $\varphi_m$ of the function $m_A(\varphi)$ is plotted as a function of $b_A = \beta_A f_A^{\rm in}$. The solid (dashed) line corresponds to $A$ being a fermion (boson).
• Figure 2: The solid line represents $\log_{10} [ (g^2_{\rm rad} - g^2_0)/g^2_0 ]$ as a function of $\log_{10} \kappa$, i.e. the fractional deviation (left over at the end of the radiation era) of the gauge coupling constants $g^2_{\rm rad} \propto B^{-1}(\varphi_{\rm rad})$ from their present values $g^2_0$, versus the curvature $\kappa$ of the function $\ln B^{-1}(\varphi)$ near its minimum. The dashed line represents an analytical estimate (when $\kappa \agt 1$) of that deviation, obtained by assuming that the phases $\theta$ of the WKB results Eq. (\ref{['eq:4.10a']}) are randomly distributed.
• Figure 3: The solid line represents $\log_{10}(\Delta a / a)_{\rm max}$ as a function of $\log_{10} \kappa$, i.e. the expected present level of violation of the equivalence principle (when comparing Uranium with a light element) as a function of the curvature $\kappa$ of the (string-loop induced) function $\ln B^{-1}(\varphi)$ near a minimum $\varphi_m$. The dashed line represents an analytical estimate (when $\kappa \agt 1$) of that violation obtained by assuming random phases $\theta$ in Eqs. (\ref{['eq:4.10a']}) and (\ref{['eq:5.6']}).