Is Alice burning or fuzzing?

Recently, Almheiri, Marolf, Polchinski and Sully (AMPS) have suggested a Gedankenexperiment to test black hole complementarity. They claim that the postulates of black hole complementarity are mutually inconsistent and choose to give up the "absence of drama" for an infalling observer. According to them the black hole is shielded by a firewall no later than Page time. This has generated some controversy. We find that an interesting picture emerges when we take into account objections from the advocates of fuzzballs. We reformulate AMPS' Gedankenexperiment in the decoherence picture of quantum mechanics and find that low energy wave packets interact with the radiation quanta rather violently while high energy wave packets do not. This is consistent with Mathur's recent proposal of fuzzball complementarity for high energy quanta falling into fuzzballs.Comment: 14 pages, 6 figures; v3: References added, discussions of some parts changed substantially, conclusions unaltere

Counting charged massless states in the (0,2) heterotic CFT/geometry connection

We use simple current techniques and their relation to orbifolds with discrete torsion for studying the (0,2) CFT/geometry duality with non-rational internal N=2 SCFTs. Explicit formulas for the charged spectra of heterotic SO(10) GUT models are computed in terms of their extended Poincar\'{e} polynomials and the complementary Poincar\'{e} polynomial which can be computed in terms of the elliptic genera. While non-BPS states contribute to the charged spectrum, their contributions can be determined also for non-rational cases. For model building, with generalizations to SU(5) and SM gauge groups, one can take advantage of the large class of Landau-Ginzburg orbifold examples.Comment: 51 pages. Acknowledgments update

Metastability in Bubbling AdS Space

We study the dynamics of probe M5 branes with dissolved M2 charge in bubbling geometries with SO(4) x SO(4) symmetry. These solutions were constructed by Bena-Warner and Lin-Lunin-Maldacena and correspond to the vacua of the maximally supersymmetric mass-deformed M2 brane theory. We find that supersymmetric probe M2 branes polarize into M5 brane shells whose backreaction creates an additional bubble in the geometry. We explicitly check that the supersymmetric polarization potential agrees with the one found within the Polchinski-Strassler approximation. The main result of this paper is that probe M2 branes whose orientation is opposite to the background flux can polarize into metastable M5 brane shells. These decay to a supersymmetric configuration via brane-flux annihilation. Our findings suggest the existence of metastable states in the mass-deformed M2 brane theory.Comment: 38 pages, 8 figure

A rough end for smooth microstate geometries

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, incorporating full backreaction, and are in fact special cases of known microstate geometries. In a near-horizon limit, they reduce to Aichelburg-Sexl shockwaves in $AdS_3 \times S^3$ 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 $j \sim \sqrt{n_1n_5}$ 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.Comment: 22 pages, 1 figure. v2: JHEP version with references adde

Journey to the Center of the Fuzzball

We study two-charge fuzzball geometries, with attention to the use of the proper duality frame. For zero angular momentum there is an onion-like structure, and the smooth D1-D5 geometries are not valid for typical states. Rather, they are best approximated by geometries with stringy sources, or by a free CFT. For non-zero angular momentum we find a regime where smooth fuzzball solutions are the correct description. Our analysis rests on the comparison of three radii: the typical fuzzball radius, the entropy radius determined by the microscopic theory, and the breakdown radius where the curvature becomes large. We attempt to draw more general lessons.Comment: 22 pages, 1 figur

Almost BPS but still not renormalized

A key feature of BPS multi-center solutions is that the equations controlling the positions of these centers are not renormalized as one goes from weak to strong coupling. In particular, this means that brane probes can capture the same information as the fully back-reacted supergravity solution. We investigate this non-renormalization property for non-supersymmetric, extremal "almost-BPS" solutions at intermediate coupling when one of the centers is considered as a probe in the background created by the other centers. We find that despite the lack of supersymmetry, the probe action reproduces exactly the equations underlying the fully back-reacted solution, which indicates that these equations also do not receive quantum corrections. In the course of our investigation we uncover the relation between the charge parameters of almost-BPS supergravity solutions and their quantized charges, which solves an old puzzle about the quantization of the charges of almost-BPS solutions.Comment: 29 pages, 1 figur

Unitarity and fuzzball complementarity: "Alice fuzzes but may not even know it!"

We investigate the recent black hole firewall argument. For a black hole in a typical state we argue that unitarity requires every quantum of radiation leaving the black hole to carry information about the initial state. An information-free horizon is thus inconsistent with unitary at every step of the evaporation process (in particular both before and after Page time). The required horizon-scale structure is manifest in the fuzzball proposal which provides a mechanism for holding up the structure. In this context we want to address the experience of an infalling observer and discuss the recent fuzzball complementarity proposal. Unlike black hole complementarity and observer complementarity which postulate asymptotic observers experience a hot membrane while infalling ones pass freely through the horizon, fuzzball complementarity postulates that fine-grained operators experience the details of the fuzzball microstate and coarse-grained operators experience the black hole. In particular, this implies that an infalling detector tuned to energy E ~ T, where T is the asymptotic Hawking temperature, does not experience free infall while one tuned to E >> T does.Comment: v3: 33 pages + citations, 8 figures, version accepted for publicatio