nLab
Nambu-Goto action

Context

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Definition

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

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

where dvol(γ *g)dvol(\gamma^* g) is the volume form of the pullback γ *g\gamma^* g of the metric tensor from XX to Σ\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 XX. For dimΣ=1dim \Sigma = 1 this is the relativistic particle, for dimΣ=2dim \Sigma = 2 the string, for dimΣ=3dim \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)