Supersymmetry and Wrapped Branes in Microstate Geometries

We consider the supergravity back-reaction of M2 branes wrapping around the space-time cycles in 1/8-BPS microstate geometries. We show that such brane wrappings will generically break all the supersymmetries. In particular, all the supersymmetries will be broken if there are such wrapped branes but the net charge of the wrapped branes is zero. We show that if M2 branes wrap a single cycle, or if they wrap a several of co-linear cycles with the same orientation, then the solution will be 1/16-BPS, having two supersymmetries. We comment on how these results relate to using W-branes to understand the microstate structure of 1/8-BPS black holes.Comment: 20 page

BPS equations and Non-trivial Compactifications

We consider the problem of finding exact, eleven-dimensional, BPS supergravity solutions in which the compactification involves a non-trivial Calabi-Yau manifold, ${\cal Y}$, as opposed to simply a $T^6$. Since there are no explicitly-known metrics on non-trivial, compact Calabi-Yau manifolds, we use a non-compact "local model" and take the compactification manifold to be ${\cal Y} = {\cal M}_{GH} \times T^2$ where ${\cal M}_{GH}$ is a hyper-K\"ahler, Gibbons-Hawking ALE space. We focus on backgrounds with three electric charges in five dimensions and find exact families of solutions to the BPS equations that have the same four supersymmetries as the three-charge black hole. Our exact solution to the BPS system requires that the Calabi-Yau manifold be fibered over the space-time using compensators on ${\cal Y}$. The role of the compensators is to ensure smoothness of the eleven-dimensional metric when the moduli of ${\cal Y}$ depend on the space-time. The Maxwell field Ansatz also implicitly involves the compensators through the frames of the fibration. We examine the equations of motion and discuss the brane distributions on generic internal manifolds that do not have enough symmetry to allow smearing.Comment: 32 pages, no figure

Resolving the Structure of Black Holes: Philosophizing with a Hammer

We give a broad conceptual review of what we have learned about black holes and their microstate structure from the study of microstate geometries and their string theory limits. We draw upon general relativity, supergravity, string theory and holographic field theory to extract universal ideas and structural features that we expect to be important in resolving the information problem and understanding the microstate structure of Schwarzschild and Kerr black holes. In particular, we emphasize two conceptually and physically distinct ideas, with different underlying energy scales: a) the transition that supports the microstate structure and prevents the formation of a horizon and b) the representation of the detailed microstate structure itself in terms of fluctuations around the transitioned state. We also show that the supergravity mechanism that supports microstate geometries becomes, in the string theory limit, either brane polarization or the excitation of non-Abelian degrees of freedom. We thus argue that if any mechanism for supporting structure at the horizon scale is to be given substance within string theory then it must be some manifestation of microstate geometries.Comment: 32 pages + reference

Doubly-Fluctuating BPS Solutions in Six Dimensions

We analyze the BPS solutions of minimal supergravity coupled to an anti-self-dual tensor multiplet in six dimensions and find solutions that fluctuate non-trivially as a function of two variables. We consider families of solutions coming from KKM monopoles fibered over Gibbons-Hawking metrics or, equivalently, non-trivial T^2 fibrations over an R3 base. We find smooth microstate geometries that depend upon many functions of one variable, but each such function depends upon a different direction inside the T^2 so that the complete solution depends non-trivially upon the whole T^2 . We comment on the implications of our results for the construction of a general superstratum.Comment: 24 page

Supersymmetric Janus Solutions in Four Dimensions

We use maximal gauged supergravity in four dimensions to construct the gravity dual of a class of supersymmetric conformal interfaces in the theory on the world-volume of multiple M2-branes. We study three classes of examples in which the $(1+1)$-dimensional defects preserve $(4,4)$, $(0,2)$ or $(0,1)$ supersymmetry. Many of the solutions have the maximally supersymmetric $AdS_4$ vacuum dual to the $\mathcal{N}=8$ ABJM theory on both sides of the interface. We also find new special classes of solutions including one that interpolates between the maximally supersymmetric vacuum and a conformal fixed point with $\mathcal{N}=1$ supersymmetry and $G_2$ global symmetry. We find another solution that interpolates between two distinct conformal fixed points with $\mathcal{N}=1$ supersymmetry and $G_2$ global symmetry. In eleven dimensions, this $G_2$ to $G_2$ solution corresponds to a domain wall across which a magnetic flux reverses orientation.Comment: 54 pages, 11 figure