Heating up the BIon

Abstract

We propose a new method to consider D-brane probes in thermal backgrounds. The method builds on the recently developed blackfold approach to higher-dimensional black holes. While D-brane probes in zero-temperature backgrounds are well-described by the Dirac-Born-Infeld (DBI) action, this method addresses how to probe thermal backgrounds. A particularly important feature is that the probe is in thermal equilibrium with the background. We apply our new method to study the thermal generalization of the BIon solution of the DBI action. The BIon solution is a configuration in flat space of a D-brane and a parallel anti-D-brane connected by a wormhole with F-string charge. In our thermal generalization, we put this configuration in hot flat space. We find that the finite temperature system behaves qualitatively different than its zero-temperature counterpart. In particular, for a given separation between the D-brane and anti-D-brane, while at zero temperature there are two phases, at finite temperature there are either one or three phases available.

Blackfolds, plane waves and minimal surfaces

“…Examples of situations where this behaviour may be the case are found in the context of BIon solutions [43,44] and M2-M5 intersections [45][46][47]. If the geometry has boundaries, this could potentially signify that the geometry near the boundary would have to be replaced by something else than (2.10) but which would smoothly connect to (2.10).…”

Forced fluid dynamics from blackfolds in general supergravity backgrounds

“…In blackfold generalizations of the fluid/gravity correspondence the long-wavelength expansion of the (super)gravity equations around black brane solutions is an affair that combines the fluid dynamical nature of black hole physics [7-9, 11, 12] with the extrinsic (elastic) dynamics [7,[13][14][15][16][17][18][19][20][21][22][23][24][25] of hypersurfaces in ambient spacetimes that is characteristic of D-brane physics. Unfortunately, even the case of black holes in flat space is sufficiently complicated and it has not yet been studied systematically beyond the first order in the derivative expansion.…”

“…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.…”

“…Analogous to [22] we focus on the large r region of the near-zone solution. In this region, the metric takes the form 17) while the field strength and dilaton are given by…”

“…the Euclidean action over a D-dimensional region Y with boundary ∂Y for q = 0 and a q = 0 becomes 17) where the boundary ∂Y is chosen to be a constant radial slice at infinity in the geometry of (4.15) and where [K] denotes the difference between the extrinsic curvature of a constant radial slice in (4.15) and the analogous radial slice in flat spacetime written in the same coordinates as in (4.15) but with an appropriate temperature redshift at infinity. Analogous to the case considered in section 3.1 of p-branes with a top-form, we construct the leading order ansatz by adding a constant gauge field C 1 to C 1 via a local gauge transformation such that, without loss of generality, the boosted gauge field (4.15) is given by…”