In physics, the Polyakov action is the two-dimensional action of a conformal field theory describing the worldsheet of a string in string theory. It was introduced by S.Deser and B.Zumino and independently by L.Brink, P.Di Vecchia and P.S.Howe (in Physics Letters B65, pgs 369 and 471 respectively), and has become associated with Alexander Polyakov after he made use of it in quantizing the string. The action reads
where is the string tension, is the metric of the target manifold, is the worldsheet metric and is the determinant of . The metric signature is chosen such that timelike directions are + and the spacelike directions are -. The spacelike worldsheet coordinate is called whereas the timelike worldsheet coordinate is called . This is also known as nonlinear sigma model.
The Polyakov action must be supplemented by the Liouville action to describe string fluctuations.
Read more about Polyakov Action: Global Symmetries, Local Symmetries, Relation With Nambu-Goto Action, Equations of Motion
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