We construct an approximate solution for an asymptotically flat, neutral, thin rotating black ring in any dimension D ≥ 5 by matching the near-horizon solution for a bent boosted black string, to a linearized gravity solution away from the horizon. The rotating black ring solution has a regular horizon of topology S 1 × S D−3 and incorporates the balancing condition of the ring as a zero-tension condition. For D = 5 our method reproduces the thin ring limit of the exact black ring solution. For D ≥ 6 we show that the black ring has a higher entropy than the Myers-Perry black hole in the ultraspinning regime. By exploiting the correspondence between ultra-spinning black holes and black membranes on a two-torus, we take steps towards qualitatively completing the phase diagram of rotating blackfolds with a single angular momentum. We are led to propose a connection between MP black holes and black rings, and between MP black holes and black Saturns, through merger transitions involving two kinds of 'pinched' black holes. More generally, the analogy suggests an infinite number of pinched black holes of spherical topology leading to a complicated pattern of connections and mergers between phases.

We develop and significantly generalize the effective worldvolume theory for higherdimensional black holes recently proposed by the authors. The theory, which regards the black hole as a black brane curved into a submanifold of a background spacetime -a blackfold-, can be formulated in terms of an effective fluid that lives on a dynamical worldvolume. Thus the blackfold equations split into intrinsic (fluid-dynamical) equations, and extrinsic (generalized geodesic embedding) equations. The intrinsic equations can be easily solved for equilibrium configurations, thus providing an efficient formalism for the approximate construction of novel stationary black holes. Furthermore, it is possible to study time evolution. In particular, the long-wavelength component of the GregoryLaflamme instability of black branes is obtained as a sound-mode instability of the effective fluid. We also discuss action principles, connections to black hole thermodynamics, and other consequences and possible extensions of the approach. Finally, we outline how the fluid/AdS-gravity correspondence is related to this formalism.

We argue that the main feature behind novel properties of higher-dimensional black holes, compared to four-dimensional ones, is that their horizons can have two characteristic lengths of very different size. We develop a long-distance world-volume effective theory that captures the black hole dynamics at scales much larger than the short scale. In this limit the black hole is regarded as a blackfold: a black brane (possibly boosted locally) whose world volume spans a curved submanifold of the spacetime. This approach reveals black objects with novel horizon geometries and topologies more complex than the black ring, but more generally it provides a new organizing framework for the dynamics of higher-dimensional black holes.

We review recent progress on the instabilities of black strings and branes both for pure Einstein gravity as well as supergravity theories which are relevant for string theory. We focus mainly on Gregory-Laflamme instabilities. In the first part of the review we provide a detailed discussion of the classical gravitational instability of the neutral uniform black string in higher dimensional gravity. The uniform black string is part of a larger phase diagram of Kaluza-Klein black holes which will be discussed thoroughly. This phase diagram exhibits many interesting features including new phases, non-uniqueness and horizontopology changing transitions. In the second part, we turn to charged black branes in supergravity and show how the Gregory-Laflamme instability of the neutral black string implies via a boost/U-duality map similar instabilities for non-and near-extremal smeared branes in string theory. We also comment on instabilities of D-brane bound states. The connection between classical and thermodynamic stability, known as the correlated stability conjecture, is also reviewed and illustrated with examples. Finally, we examine the holographic implications of the Gregory-Laflamme instability for a number of nongravitational theories including Yang-Mills theories and Little String Theory.

We argue that the Dirac-Born-Infeld (DBI) action coupled to a tachyon, that is known to reproduce some aspects of open string dynamics, can be obtained from open string theory in a certain limit, which generalizes the limit leading to the usual DBI action. This helps clarify which aspects of the full open string theory are captured by this action. 4/03

We initiate a systematic scan of the landscape of black holes in any spacetime dimension using the recently proposed blackfold effective worldvolume theory. We focus primarily on asymptotically flat stationary vacuum solutions, where we uncover large classes of new black holes. These include helical black strings and black rings, black odd-spheres, for which the horizon is a product of a large and a small sphere, and non-uniform black cylinders. More exotic possibilities are also outlined. The blackfold description recovers correctly the ultraspinning Myers-Perry black holes as ellipsoidal even-ball configurations where the velocity field approaches the speed of light at the boundary of the ball. Helical black ring solutions provide the first instance of asymptotically flat black holes in more than four dimensions with a single spatial U(1) isometry. They also imply infinite rational non-uniqueness in ultraspinning regimes, where they maximize the entropy among all stationary single-horizon solutions. Moreover, static blackfolds are possible with the geometry of minimal surfaces. The absence of compact embedded minimal surfaces in Euclidean space is consistent with the uniqueness theorem of static black holes.

We compute exact 2-and 3-point functions of chiral primaries in fourdimensional N = 2 superconformal field theories, including all perturbative and instanton contributions. We demonstrate that these correlation functions are nontrivial and satisfy exact differential equations with respect to the coupling constants. These equations are the analogue of the tt * equations in two dimensions. In the SU(2) N = 2 SYM theory coupled to 4 hypermultiplets they take the form of a semi-infinite Toda chain. We provide the complete solution of this chain using input from supersymmetric localization. To test our results we calculate the same correlation functions independently using Feynman diagrams up to 2-loops and we find perfect agreement up to the relevant order. As a spin-off, we perform a 2-loop check of the recent proposal of arXiv:1405.7271 that the logarithm of the sphere partition function in N = 2 SCFTs determines the Kähler potential of the Zamolodchikov metric on the conformal manifold. We also present the tt * equations in general SU(N ) N = 2 superconformal QCD theories and comment on their structure and implications.

We develop the effective worldvolume theory for the dynamics of black branes with charges of the kind that arise in many supergravities and low-energy limits of string theory. Using this theory, we construct numerous new rotating black holes with charges and dipoles of D-branes, fundamental strings and other branes. In some instances, the black holes can be dynamically stable close enough to extremality. Some of these black holes, such as those based on the D1-D5-P system, have extremal, non-supersymmetric limits with regular horizons of finite area and a wide variety of horizon topologies and geometries.