The Nambu-Goto action is an action functional for sigma-models with target space a (pseudo) Riemannian manifold : it is the induced volume functional
where is the volume form of the pullback of the metric tensor from to , and where (the brane-“tension”, e.g. the string tension for ) is an inverse unit of length to the power the dimension .
Let
(for p-brane dynamics);
a compact smooth manifold of dimension (worldvolume).
the diffeological space of smooth functions .
For the induced “proper volume” or Nambu-Goto action of is the integral over of the volume form of the pullback of the target space metric to .
Notice that the rank-2 tensor is in general not degenerate (unless is an embedding), hence is in general not, strictly speaking a pseudo-Riemannian metric on , but nevertheless it induces a volume form by the standard formula, only that this allowed to vanish pointwise (and even globally, for instance if is constant on a single point). In the literature is usually written as .
The NG is classically equivalent to the Polyakov action with “worldvolume cosmological constant”. See at Polyakov action – Relation to Nambu-Goto action.
The NG-action serves as the kinetic action functional of the sigma-model that described a fundamental brane propagating on . For this is the relativistic particle, for the string, for the membrane.
for more on brane tension see also Worldsheet and brane instantons
The Nambu-Goto action functional is named after Yoichiro Nambu.
Detailed discussion of the relation to the Polyakov action and the Dirac-Born-Infeld action is in
One string theory textbook that deals with the Nambu-Goto action in a bit more detail than usual is
Last revised on December 21, 2022 at 11:44:56. See the history of this page for a list of all contributions to it.