Mass scales in string and M-theory

TL;DR

This paper reviews how different mass scales in string and M-theory relate, exploring large extra dimensions, low string scales, and their implications for particle physics and gravity experiments.

Contribution

It provides a comprehensive analysis of possible large volume compactifications and low string scale scenarios, including their physical motivations and experimental implications.

Findings

Large longitudinal dimensions imply strong coupling unless tension is near compactification scale.

Low string scale models require extra large transverse dimensions or infinitesimal string coupling.

TeV-scale strings and large extra dimensions can address the hierarchy problem and supersymmetry breaking.

Abstract

I review the relations between mass scales in various string theories and in M-theory. I discuss physical motivations and possible consistent realizations of large volume compactifications and low string scale. Large longitudinal dimensions, seen by Standard Model particles, imply in general that string theory is strongly coupled unless its tension is close to the compactification scale. Weakly coupled, low-scale strings can in turn be realized only in the presence of extra large transverse dimensions, seen through gravitational interactions, or in the presence of infinitesimal string coupling. In the former case, quantum gravity scale is also low, while in the latter, gravitational and string interactions remain suppressed by the four-dimensional Planck mass. There is one exception in this general rule, allowing for large longitudinal dimensions without low string scale, when Standard Model is embedded in a six-dimensional fixed-point theory described by a tensionless string. Extra dimensions of size as large as TeV$^{-1}\simeq 10^{-16}$ cm are motivated from the problem of supersymmetry breaking in string theory, while TeV scale strings offer a solution to the gauge hierarchy problem, as an alternative to softly broken supersymmetry or technicolor. I discuss these problems in the context of the above mentioned string realizations, as well as the main physical implications both in particle accelerators and in experiments that measure gravity at sub-millimeter distances.