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In physics, the Polyakov action is an action of the two-dimensional conformal field theory describing the worldsheet of a string in string theory. It was introduced by Stanley Deser and Bruno Zumino and independently by L. Brink, P. Di Vecchia and P. S. Howe in 1976,[1][2] and has become associated with Alexander Polyakov after he made use of it in quantizing the string in 1981.[3] The action reads:
where is the string tension, is the metric of the target manifold, is the worldsheet metric, its inverse, 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 the nonlinear sigma model.[4]
The Polyakov action must be supplemented by the Liouville action to describe string fluctuations.