# Momentum conservation under a Gauge Parametrization in string theory

1. May 1, 2010

### benbenny

Im reading "A first course in String Theory" by Zwiebach and it says that when applying a 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 as I understand, so how does applying the general \tau gauge make it so that it is. How can we chose a gauge that will conserve momentum on the string. The string is still going to be connected to a brane, and without considering the dynamics of the brane I dont see how this can be ensured.

Thanks,

B