The string scale and the Planck scale

TL;DR

This paper examines the relationship between the string scale and the Planck scale within heterotic string theory, revealing a significant scale discrepancy and implications for force strengths at high energies.

Contribution

It provides a detailed calculation of the ratio between the string scale and the Planck scale, highlighting the implications for gravitational and gauge interactions in string/M-theory.

Findings

The Planck mass exceeds the string scale by a factor of approximately 61.9.

A specific numerical relation between the Planck and string scales is established.

The relative strength of graviton to vector exchange is greater in the string/M-theory phase.

Abstract

A particle spectrum below the string scale in accordance with predictions from heterotic string theory yields a Planck mass $m_{Pl}=(8\pi G_N)^{-1/2}$ which exceeds the string scale by a factor $\simeq 61.9$. A Planck mass $m_{Pl}=2.43\times 10^{18}$ GeV then corresponds to a string scale $m_s=3.9\times 10^{16}$ GeV. Such a low value for the string scale in turn implies that the relative strength of graviton and vector exchange in the string/M-theory phase exceeds the corresponding ratio in the low energy field theory.