  D-branes with a U-shaped geometry, like the D8 flavor branes in the
Sakai-Sugimoto model of QCD, are encountered frequently in holographic
backgrounds. We argue that the commonly used DBI action is inadequate as an
effective field theory description of these branes, because it misses a crucial
component of the low-energy dynamics: a light complex scalar mode. Following an
idea of Erkal, Kutasov and Lunin we elaborate on an effective description based
on the abelian tachyon-DBI action which incorporates naturally the non-local
physics of the complex scalar mode. We demonstrate its power in a context where
an explicit worldsheet description of the open string dynamics exists
--hairpin-branes in the background of NS5-branes. Our results are relevant for
the holographic description of chiral symmetry breaking and bare quark mass in
QCD and open string tachyon condensation in curved backgrounds.
