nLab
string length scale

Contents

Contents

Idea

In perturbative string theory, the string length scale s\ell_s is a unit of length which sets the scale for the extension of strings described by sigma-model worldsheet field theories. Specifically, the Nambu-Goto action for the string is nothing but the relativistic volume-functional, and the string length determines in which units the volume is measured.

The square of the string length is known as the Regge slope and traditionally denoted by α \alpha^\prime:

α = s 2. \alpha^\prime \;=\; \ell_s^2 \,.

The inverse of the string length squared/Regge slope is called the string tension, traditionally denoted

T s=12πα =12π s 2. T_s \;=\; \frac{1}{2\pi \alpha^\prime} = \frac{1}{2 \pi \ell_s^2} \,.

This way the Nambu-Goto action for the string with proper units attached is

L NG=Tvol Σ, L_{NG} \;=\; T vol_{\Sigma} \,,

where vol Σvol_{\Sigma} is the (induced) volume form on the worldsheet Σ\Sigma.

Properties

Relation to Planck length and string coupling

For discussion of relation to Planck length and string coupling constant see at non-perturbative effect the section Worldsheet and brane instantons

Vanishing tension limit

In the limit T s0T_s \to 0, s\ell_s \to \infty of vanishing string tension, string field theory is supposed to become Vasiliev’s higher spin gauge theory. See there for more.

fundamental scales (fundamental physical units)

References

For instance:

Last revised on April 12, 2020 at 17:11:36. See the history of this page for a list of all contributions to it.