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D-branes also arise in perturbative string theory on flat backgrounds as hypersurfaces in space on which strings can end due to Dirichlet boundary conditions. The equivalence of D-branes and p-branes is completely independent from the AdS/CFT correspondence and was discovered before the correspondence by Polchinski in 1995 (see here). D-branes and p-branes ...


For a quick (and somewhat dirty) way of deriving the bound, do the following: Recall, that in Poincaré coordinates, the metric of $AdS_{d+1}$ is $$ ds=\frac{1}{z^2}\left(dz^2+\eta^{\mu\nu}dx^\mu dx^\nu\right). $$ The equation of motion for a scalar is $$ (\Box-m^2)\,\phi(z,x)=0, $$ where $\Box=\frac{1}{\sqrt{-g}}\partial_a \sqrt{-g}g^{ab}\partial_b$. ...

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