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nLab

string length scale

Contents
### Context

#### String theory

### Ingredients

### Critical string models

### Extended objects

### Topological strings

## Backgrounds

## Phenomenology

# Contents

## Idea

In perturbative string theory, the *string length scale* $\ell_s$ 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 $\alpha^\prime$:

$\alpha^\prime \;=\; \ell_s^2
\,.$

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

$T_s \;=\; \frac{1}{2\pi \alpha^\prime} = \frac{1}{2 \pi \ell_s^2}
\,.$

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

$L_{NG} \;=\; T vol_{\Sigma}
\,,$

where $vol_{\Sigma}$ is the (induced) volume form on the worldsheet $\Sigma$.

## 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 $T_s \to 0$, $\ell_s \to \infty$ 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.
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