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A open bosonic string between two parallel branes seems to obey formulae such as

$M^2 = \big((n + {\theta_i - \theta_j \over 2 \pi}) {R' \over \alpha'}\big)^2 + {N-1 \over \alpha'} $

So that the difference $\theta_i - \theta_j$ is the distance between branes. Now I wonder, which is the formula for the superstring stretched between two parallel branes? Is it the same?

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It's similar --

$${m^2} = \left( {N - a} \right) + {\left( {\frac{y}{{2\pi }}} \right)^2}$$

The important difference is that the number operator and normal ordering constant change for a superstring, and vary by sector.

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