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#3 Nambu-Goto action

Given a d-dimensional manifold \mathcal{M}_{d} with a metric G_{\mu\nu}(X), a string is a one-dimensional object moving inside \mathcal{M}_{d}. The Nambu-Goto action describes the dynamics of these objects. It’s strongly inspired in the relativistic dynamics of a point particle.

A point particle describes a curve when it’s moving through space and time. Such curve (its trajectory) depends on a single parameter, usually the proper time. Likewise, a string describes a two-dimensional surface called world sheet, and depends on two parameters X^{\mu}(\tau,\sigma). Even though the role of both parameters is arbitrary, one can think of \tau as the proper time, and, for any given \tau, \sigma would label each one of the points that the string is made of.

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