Abstract
Supersymmetric microstate geometries with five non-compact dimensions have recently been shown by Eperon, Reall, and Santos (ERS) to exhibit a non-linear instability featuring the growth of excitations at an “evanescent ergosurface” of infinite redshift. We argue that this growth may be treated as adiabatic evolution along a family of exactly supersymmetric solutions in the limit where the excitations are Aichelburg-Sexl-like shockwaves. In the 2-charge system such solutions may be constructed explicitly, incorpo-rating full backreaction, and are in fact special cases of known microstate geometries. In a near-horizon limit, they reduce to Aichelburg-Sexl shockwaves in AdS3 × S3 propagating along one of the angular directions of the sphere. Noting that the ERS analysis is valid in the limit of large microstate angular momentum j, we use the above identification to interpret their instability as a transition from rare smooth microstates with large angular momentum to more typical microstates with smaller angular momentum. This entropic driving terminates when the angular momentum decreases to jsim sqrt{n_1{n}_5} where the density of microstates is maximal. We argue that, at this point, the large stringy corrections to such microstates will render them non-linearly stable. We identify a possible mechanism for this stabilization and detail an illustrative toy model.
Highlights
√ driving terminates when the angular momentum decreases to j ∼ n1n5 where the density of microstates is maximal
Supersymmetric microstate geometries with five non-compact dimensions have recently been shown by Eperon, Reall, and Santos (ERS) to exhibit a non-linear instability featuring the growth of excitations at an “evanescent ergosurface” of infinite redshift
Drive the initially smooth horizonless microstate geometry to an almost-supersymmetric black hole with the same brane charges as the microstate geometry but with different angular momenta. They suggested that the endstate of the instability might be a nearextremal black hole [24] or a black ring [25]. To support this argument one may note that as the solution shrinks it is described by the duality cascade of [21], but since the evanescent ergosurface is a consequence of supersymmetry it persists in every duality frame and so the ERS instability argument continues to apply
Summary
Let us consider IIB string theory compactified to M 1,4 × S1 × T 4, with n1 D1 branes wrapping the S1 and n5 D5 branes wrapping S1 × T 4. The complete theory with target space (T 4)N /SN has N copies of the c = 6 CFT with states symmetrized between the N copies. The state |N1 = σ1N1|0 with N1 = N and all other modes zero is the unique completely untwisted state, corresponding to the Ramond ground state with maximal R-charge, and to a state of maximal angular momentum jmax = n1n5. Before proceeding to discuss geometries, we remind the reader that states in the Ramond sector can be mapped to states in the Neveu-Schwarz sector via a symmetry of theories with N ≥ 2 in 2 dimensions known as spectral flow. Ramond ground states of non-maximal R-charge map to chiral primaries in the NS sector. On the gravity side spectral flow of the near-horizon limit for the corresponding solution will give AdS3 × S3 in global coordinates
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