# #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.