  We propose an open/closed string duality in general backgrounds extending
previous ideas about open string completeness by Ashoke Sen. Our proposal sets
up a general version of holography that works in gravity as a tomographic
principle. We argue, in particular, that previous expectations of a
supergravity/Dirac-Born-Infeld (DBI) correspondence are naturally embedded in
this conjecture and can be tested in a well-defined manner. As an example, we
consider the correspondence between open string field theories on extremal
D-brane setups in flat space in the large-N, large 't Hooft limit, and
asymptotically flat solutions in ten-dimensional type II supergravity. We focus
on a convenient long-wavelength regime, where specific effects of higher-spin
open string modes can be traced explicitly in the dual supergravity
computation. For instance, in this regime we show how the full abelian DBI
action arises from supergravity as a straightforward reformulation of
relativistic hydrodynamics. In the example of a (2+1)-dimensional open string
theory this reformulation involves an abelian Hodge duality. We also point out
how different deformations of the DBI action, related to higher-derivative
corrections and non-abelian effects, can arise in this context as deformations
in corresponding relativistic hydrodynamics.
