# The stability of D-Brane

In "String Theory and M-Theory: a modern introduction" by K.Becker, M. Becker and J.H.Schwarz, they say that BPS D-brane is stable as it preserves half of the Supersymmetry. I really want to understand more about this statement and see detail calculations. What is the mechanism of D-brane stability? Is there any derivation for the instability of space-filling D-brane (so that open string tachyon will be eliminated from the theory)?

Thank you.

As an analogy, note that the electron has to be stable because there exists no lighter $Q=-e$ object than the electron (and positron).
BPS objects are either those preserving some (enough) supersymmetry; or objects saturating the BPS bound $M=Q$, schematically speaking (for branes, it's the tension equal to the charge density; coefficients should be inserted everywhere). These conditions are equivalent because $$\{Q,Q\} = M-Z$$ schematically, for some conserved supercharge $Q$. So the expectation value of $\{Q,Q\}$ in the BPS state is zero – because $Q$ annihilates the state – but it's also equal to $M-Z$ which means that the mass is equal to the charge. For non-BPS states, we have the strict $M\gt Z$. Here, $Z$ is the conserved central charge.