  Recently it has been observed that branes in geometric engineering and
holography have a striking connection with generalized global symmetries. In
this paper we argue that branes, in a certain topological limit, not only
furnish the symmetry generators, but also encode the so-called Symmetry
Topological Field Theory (or SymTFT). For a $d$-dimensional QFT, this is a
$(d+1)$-dimensional topological field theory, whose topological defects encode
both the symmetry generators (invertible or non-invertible) and the generalized
charges. Mathematically, the topological defects form the Drinfeld center of
the symmetry category of the QFT. In this paper we derive the SymTFT and the
Drinfeld center topological defects directly from branes. Central to the
identification of these are Hanany-Witten brane configurations, which encode
both topological couplings in the SymTFT and the generalized charges under the
symmetries. We exemplify the general analysis with examples of QFTs realized in
geometric engineering or holography.
