# Contents

## Definition

The Nambu-Goto action is an action functional for sigma-models with target space a (pseudo) Riemannian manifold $(X,g)$: it is the induced volume functional

$S_{NG} : (\Sigma \stackrel{\gamma}{\to} X) \mapsto \int_\Sigma dvol(\gamma^* g) \,,$

where $dvol(\gamma^* g)$ is the volume form of the pullback $\gamma^* g$ of the metric tensor from $X$ to $\Sigma$.

This is classically equivalent (…) to the Polyakov action.

## Applications

The NG-action serves as the kinetic action functional of the sigma-model that described a fundamental brane propagating on $X$. For $dim \Sigma = 1$ this is the relativistic particle, for $dim \Sigma = 2$ the string, for $dim \Sigma = 3$ the membrane.

## References

The Nambu-Goto action functional is named after Yoichiro Nambu.

One string theory textbook that deals with the Nambu-Goto action in a bit more detail than usual is

Revised on March 6, 2014 13:07:16 by Urs Schreiber (89.204.135.180)