Momentum conservation under a Gauge Parametrization in string theory

[benbenny]

Second attempt here to get an answer, I am really lost on this.
Im reading "A first course in String Theory" by Zwiebach and it says that when applying a general $$\tau$$ gauge parametrization in the form of $$n_\mu X^\mu = \lambda \tau$$ we can take the vector $$n_\mu$$ so that for open strings connected to branes (fixed end points) $$n^\mu \mathcal{P}^\tau _\mu$$, is conserved.

But in general momentum is not conserved over the string for dirchlet boundary conditions, without taking into consideration the dynamics of the D-brane, as I understand, so how does applying the general \tau gauge make it so that it is essentially conserved? How can we choose a gauge that will conserve momentum on the string. The string is still going to be connected to a brane after all. I am trying to understand the physical interpretation of this statement.

Thanks,

B

 

[NateD]

The general \tau gauge parametrization is a way to choose a coordinate system that will make it easier to analyze the physical behavior of the string. The vector n_\mu describes the direction of the coordinate system, and its components are chosen such that momentum is conserved over the string when it is connected to branes (fixed endpoints). This is done by selecting n^\mu \mathcal{P}^\tau_\mu to be proportional to a conserved quantity. In this way, the momentum of the string is effectively conserved even when Dirichlet boundary conditions are applied, since the dynamics of the D-brane are taken into consideration.