Open/closed string duality and relativistic fluids

Abstract

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.

Forced fluid dynamics from blackfolds in general supergravity backgrounds

“…They provide a strong-coupling description of the effective longwavelength dynamics of the abelian, center-of-mass degrees of freedom of D/M-branes. In accordance with this expectation it was demonstrated in specific examples in [30] that the leading order blackfold equations of extremal p-brane configurations in string theory are equivalent to the DBI equations that describe long-wavelength dynamics of D-branes.…”

“…The disadvantage of this approach is the implementation of further approximations; the advantage is the possibility of a wider, more flexible application of the method. We briefly comment on the open-closed string interpretation of these additional approximations in the context of the proposal [30]. We conclude section 5 with a list of interesting open problems that could be treated in a natural continuation of this work.…”

“…It was shown in [30] that the combined set of equations (3.36), (3.41) in a trivial flat space background at extremality are equivalent to the equations of motion of the (p + 1)-dimensional DBI action with an electric field constraint (see eq. (7.34) in [30]).…”

“…Another motivation for this work is the recent proposal [30] (see also [31] for related independent work building on [17,32,33]) that the effective hydrodynamic description of black brane solutions in the blackfold formalism is connected to the underlying microscopic description of D/M-branes in string/M-theory via a general open/closed string duality that works in many cases in gravity as a tomographic principle. In the proposal of ref.…”

“…In the proposal of ref. [30] the abelian hydrodynamic blackfold equations are conjectured to be effective equations of singleton dynamics. They provide a strong-coupling description of the effective longwavelength dynamics of the abelian, center-of-mass degrees of freedom of D/M-branes.…”