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.

References

For instance:

Last revised on May 18, 2019 at 14:29:55. See the history of this page for a list of all contributions to it.