Emil J. Martinec

A bstract: We construct a large new class of BPS supergravity solutions parametrized by arbitrary chiral wave profiles on fundamental string and Neveu-Schwarz fivebrane sources. The effective action approach we employ describes the regime where the brane sources are slightly separated. String probes see these backgrounds as smooth and effectively capped off at the scale of that separation. Within the space of solutions is a large ensemble of ultracompact objects exhibiting many of the features of extremal BTZ black holes, in particular having a deep AdS ₂ throat. We present the details of solutions with circular source profiles, and compare them to known superstratum geometries. The separation of the sources makes them structurally more like BPS fivebrane stars than like extremal black hole microstates. When evaluated on the supergravity background, the brane effective action governs (chaotic) near-BPS dynamics, and exhibits a collective mode analogous to the Schwarzian mode of AdS ₂ black holes. Finally, we discuss the approach to the black hole phase as the sources coalesce, in which the semiclassical approximation breaks down due to the appearance of light D-brane excitations; this bulk realization of the fivebrane deconfinement transition connects directly to the Hawking-Page transition.

A bstract: Supergravity solutions describing supersymmetric rotating bound states of NS fivebranes, fundamental strings and momentum can sometimes have an ergoregion but no horizon. In such supersymmetric ergoregions, there is an unusual feature that there exist BPS “excitations” that cost negative (or zero) energy as measured from asymptotic infinity. We study the spectrum of supergravity and string excitations of these backgrounds using their worldsheet description as gauged Wess-Zumino-Witten (WZW) models, and construct their holographic map to transitions in the dual spacetime CFT. The backgrounds generically contain orbifold singularities, and we exhibit vertex operators corresponding to twisted sector ground states localized at the orbifold fixed points. The gauged WZW model thus provides a valuable tool to explore the stringy structure of such heavy BPS states in AdS ₃ / CFT ₂ .

A bstract: In AdS ₃ /CFT ₂ duality, there are large families of smooth, horizonless microstate geometries that correspond to heavy pure states of the dual CFT. The metric and fluxes are complicated functions of up to five coordinates. There are also many duals of heavy pure states that cannot be described in supergravity, but only admit a worldsheet description. Extracting the physical properties of these solutions is technically challenging. In this paper, we show that there are much simpler effective descriptions of these solutions that capture many of their stringy and geometrical features, at the price of sacrificing supergravity smoothness. In particular, the effective description of some families of superstrata, and of certain worldsheet solutions, is given by easy-to-construct three-center solutions. For example, the effective description of a superstratum with a long AdS ₂ throat is a scaling, three-center solution in which the momentum wave is collapsed to a singular source at one of the three centers. This also highlights how momentum migrates away from the supertube locus in the back-reacted geometry. Our results suggest that effective descriptions can be extended to more general microstates, and that many singular multi-center solutions can in fact correspond to effective descriptions of smooth horizonless microstructure.

In AdS$_3$/CFT$_2$ duality, there are large families of smooth, horizonless microstate geometries that correspond to heavy pure states of the dual CFT. The metric and fluxes are complicated functions of up to five coordinates. There are also many duals of heavy pure states that cannot be described in supergravity, but only admit a worldsheet description. Extracting the physical properties of these solutions is technically challenging. In this paper, we show that there are much simpler effective descriptions of these solutions that capture many of their stringy and geometrical features, at the price of sacrificing supergravity smoothness. In particular, the effective description of some families of superstrata, and of certain worldsheet solutions, is given by easy-to-construct three-center solutions. For example, the effective description of a superstratum with a long AdS$_2$ throat is a scaling, three-center solution in which the momentum wave is collapsed to a singular source at one of the three centers. This also highlights how momentum migrates away from the supertube locus in the back-reacted geometry. Our results suggest that effective descriptions can be extended to more general microstates, and that many singular multi-center solutions can in fact correspond to effective descriptions of smooth horizonless microstructure.

An effective action for NS5-branes coupled to supergravity is used to derive the full 10d form of horizon-free BPS solutions of fivebranes carrying momentum waves, including both transverse scalar and internal gauge excitations of the branes. When internal modes are highly excited, we find solutions that plausibly mediate the transition between the Coulomb phase of NS5-branes and the black hole phase. We also compute the two-point functions of fivebrane density fluctuations and of gravitons absorbed by the branes. Finally, we begin an exploration of near-BPS perturbations of the fivebrane ensemble, and propose the use of the brane+bulk effective action as a tool to explore the black hole phase, even in the AdS decoupling limit.

Worldsheet string theory is solvable for a variety of backgrounds involving Neveu-Schwarz fivebranes, in terms of gauged nonlinear sigma models on group manifolds. We compute the worldsheet torus partition function of these models, and propose gauging of null isometries as a unifying principle and conceptual framework for this large family of string backgrounds. In the process, we explain how partition functions of asymmetrically gauged Wess-Zumino-Witten models can be computed from the path integral, and organize and systematize various results scattered throughout the literature.

Worldsheet string theory is solvable for a variety of backgrounds involving Neveu-Schwarz fivebranes, in terms of gauged nonlinear sigma models on group manifolds. We compute the worldsheet torus partition function of these models, and propose gauging of null isometries as a unifying principle and conceptual framework for this large family of string backgrounds. In the process, we explain how partition functions of asymmetrically gauged Wess-Zumino-Witten models can be computed from the path integral, and organize and systematize various results scattered throughout the literature.

We study ensembles of 1/2-BPS bound states of fundamental strings and NS-fivebranes (NS5-F1 states) in the AdS decoupling limit. We revisit a solution corresponding to an ensemble average of these bound states, and find that the appropriate duality frame for describing the near-source structure is the T-dual NS5-P frame, where the bound state is a collection of momentum waves on the fivebranes. We find that the fivebranes are generically well-separated; this property results in the applicability of perturbative string theory. The geometry sourced by the typical microstate is not close to that of an extremal non-rotating black hole; instead the fivebranes occupy a ball whose radius is parametrically much larger than the “stretched horizon” scale of the corresponding black hole. These microstates are thus better characterized as BPS fivebrane stars than as small black holes. When members of the ensemble spin with two fixed angular potentials about two orthogonal planes, we find that the spherical ball of the non-rotating ensemble average geometry deforms into an ellipsoid. This contrasts with ring structures obtained when fixing the angular momenta instead of the angular potentials; we trace this difference of ensembles to large fluctuations of the angular momentum in the ensemble of fixed angular potential.