# Does String Theory Predict more than Four Forces?

String theory literature tells us that ST predicts the four forces: weak, strong, EM, and gravity. What it fails to tell us is if that's all the forces it predicts. Might there be a fifth force that ST predicts, but was thrown out because there is no observable evidence in 4D space that a fifth force exits?

Might that fifth force, if there is one, account for the so-called dark energy in the universe?

Greene, Witten, Kaku, and others on the string train all mention the "four forces" unified by ST. But none mentions if only those four forces are predicted by ST. Might it be possible the fifth and higher forces predicted by ST are simply not mentioned because there is no evidence in the standard model of a fifth or higher forces.

A "fifth force" can be given by a scalar field. This field arises in many theories, for example from the dilaton scalar field of string theory, that is non minimally coupled to $R$ in the action.

In the low energy limit we can phenomenologically treat string theory as a Scalar Tensor Theories of Gravitation (see the Wikipedia Link for details) in which you replace the Einstein-Hilbert action of GR for:

$\mathcal{L}_{GR}=\sqrt{-g} R \longrightarrow \mathcal{L}_{STT}=\sqrt{-g}A(\phi) R$

where $A$ is a generic function of the scalar field that fix your model. Now, if you do a conformal transformation $g_{\mu\nu}=A^{2}(\phi(x))g_{\mu\nu}^{\ E}$ you go to the so called Einstein Frame:

$\mathcal{L}_{STT}^E=\sqrt{-g_E} R_E$

in which $R_E$ is calculated with $g_{\mu\nu}^{\ E}$. It may seem that you are in the usual GR, but if you calculate the geodesic equation you find something like:

$\frac{d^2x^{\lambda}}{ds^2}+\Gamma_{\mu\nu}^{\lambda}\frac{dx^{\mu}}{ds}\frac{dx^{\nu}}{ds}=F(\phi)$

with $F$ different from zero. The extra term on the right is like a new fifth force, that a "freely falling" particle can feel. If you want, you can see this as a correction to the $1/r^2$ scaling of the force in newtonian gravity.

Some references:

-The Confrontation between General Relativity and Experiment, Clifford M. Will, Living Rev. Relativity, 17, (2014), 4. LINK

-The Search for Non-Newtonian Gravity, E. Fischbach, C. Talmadge (1999)

some theories propose that the infalton field is actually the same a dark energy,, if that were correct, then we would have a fifth field (force might not be correct in this context) that ineracts with the other four. And who knows what else, dark matter might have lots of forces that are invisible to us because they just do not inetract with the four we do.