Polyakov action

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 'A locally supersymmetric and reparametrization invariant action for the spinning string', Physics Letters B, 65, pp. 369 and 471 respectively), and has become associated with Alexander Polyakov after he made use of it in quantizing the string (in 'Quantum geometry of the bosonic string', Physics Letters B, 103, 1981, p. 207). The action reads 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 'A locally supersymmetric and reparametrization invariant action for the spinning string', Physics Letters B, 65, pp. 369 and 471 respectively), and has become associated with Alexander Polyakov after he made use of it in quantizing the string (in 'Quantum geometry of the bosonic string', Physics Letters B, 103, 1981, p. 207). The action reads where T {displaystyle T} is the string tension, g μ ν {displaystyle g_{mu u }} is the metric of the target manifold, h a b {displaystyle h_{ab}} is the worldsheet metric, h a b {displaystyle h^{ab}} its inverse, and h {displaystyle h} is the determinant of h a b {displaystyle h_{ab}} . The metric signature is chosen such that timelike directions are + and the spacelike directions are –. The spacelike worldsheet coordinate is called σ {displaystyle sigma } whereas the timelike worldsheet coordinate is called τ {displaystyle au } . This is also known as nonlinear sigma model. The Polyakov action must be supplemented by the Liouville action to describe string fluctuations.