A new supersymmetric black hole solution of five-dimensional supergravity is presented. It has an event horizon of topology S 1 × S 2 . This is the first example of a supersymmetric, asymptotically flat black hole of non-spherical topology. The solution is uniquely specified by its electric charge and two independent angular momenta. These conserved charges can be arbitrarily close, but not exactly equal, to those of a supersymmetric black hole of spherical topology.A major success of string theory is the statisticalmechanical explanation of the Bekenstein-Hawking entropy of certain supersymmetric black holes. The original example is the five-dimensional black hole studied in [1]. This is also the simplest example, as it carries the minimum number of net charges necessary to have a finite-area regular horizon, namely D1-and D5-brane charges and linear momentum along an internal direction. A generalized solution with the same charges and equal angular momenta in two orthogonal planes was discovered, and its entropy microscopically reproduced, by Breckenridge, Myers, Peet and Vafa (BMPV) [2], thus extending the success of [1] to rotating black holes with a single independent rotation parameter.The BMPV black hole has a topologically spherical event horizon. It has recently been realized that this is not true of all five-dimensional rotating black holes: the vacuum Einstein equations admit a (nonsupersymmetric) black ring solution, with horizon topology S 1 × S 2 [3]. The existence of black rings raises the question of whether there are any supersymmetric black holes in five dimensions other than BMPV.In [4] it was proven that the geometry of the event horizon of any supersymmetric black hole of minimal fivedimensional supergravity must be (i) T 3 , (ii) S 1 × S 2 or (iii) (possibly a quotient of) a homogeneously squashed S 3 . It was also proven that the only asymptotically flat supersymmetric solution with horizon geometry (iii) is the BMPV black hole (which reduces to a solution of minimal supergravity when its three charges are set equal). The purpose of this letter is to present a solution of type (ii), that is, a supersymmetric black ring. Such a solution was conjectured to exist in [5] motivated by the work of [6]. This is the first example of an asymptotically flat supersymmetric solution with a regular event horizon of non-spherical topology. It possesses a richer structure than the BMPV solution, which we will see arises as a particular case. It is parametrized by its electric charge and two independent angular momenta, which illustrates the fact that supersymmetry imposes no constraint on the angular momenta. It also has a non-vanishing magnetic dipole, which is fixed by the asymptotic charges and therefore is not an independent parameter. Some black rings are believed to be unstable [3] but supersymmetry should ensure that this new solution is stable.Our solution corresponds to taking equal values for the three charges (D1, D5 and momentum) and three dipoles (D1, D5 and Kaluza-Klein monopole) of a more ...

Using the inverse scattering method we construct an exact stationary asymptotically flat 4+1-dimensional vacuum solution describing "black saturn": a spherical black hole surrounded by a black ring. Angular momentum keeps the configuration in equilibrium. Black saturn reveals a number of interesting gravitational phenomena: (1) The balanced solution exhibits 2-fold continuous non-uniqueness for fixed mass and angular momentum;(2) Remarkably, the 4+1d Schwarzschild black hole is not unique, since the black ring and black hole of black saturn can counter-rotate to give zero total angular momentum at infinity, while maintaining balance; (3) The system cleanly demonstrates rotational framedragging when a black hole with vanishing Komar angular momentum is rotating as the black ring drags the surrounding spacetime. Possible generalizations include multiple rings of saturn as well as doubly spinning black saturn configurations.

We present supergravity solutions for 1/8-supersymmetric black supertubes with three charges and three dipoles. Their reduction to five dimensions yields supersymmetric black rings with regular horizons and two independent angular momenta. The general solution contains seven independent parameters and provides the first example of non-uniqueness of supersymmetric black holes. In ten dimensions, the solutions can be realized as D1-D5-P black supertubes. We also present a worldvolume construction of a supertube that exhibits three dipoles explicitly. This description allows an arbitrary cross-section but captures only one of the angular momenta.

We examine the gluon scattering amplitude in N = 4 super Yang-Mills at finite temperature with nonzero R-charge densities, and in Non-Commutative gauge theory at finite temperature. The gluon scattering amplitude is defined as a light-like Wil-son loop which lives at the horizon of the T-dual black holes of the backgrounds we consider. We study in detail a special amplitude, which corresponds to forward scattering of a low energy gluon off a high energy one. For this kinematic configuration in the considered backgrounds, we find the corresponding minimal surface which is directly related to the gluon scattering amplitude. We find that for increasing the chemical potential or the non-commutative parameter, the on-shell action corresponding to our Wilson loop in the T-dual space decreases. For all of our solutions the length of the short side of the Wilson loop is constrained by an upper bound which depends on the temperature, the R-charge density and the non-commutative parameter. Due to this constraint, in the limit of zeroth temperature our approach breaks down since the upper bound goes to zero, while by keeping the temperature finite and letting the chemical potential or the non-commutative parameter to approach to zero the limit is smooth.

We study n-point tree amplitudes of N = 4 super Yang-Mills theory and N = 8 supergravity for general configurations of external particles of the two theories. We construct generating functions for n-point MHV and NMHV amplitudes with general external states. Amplitudes derived from them obey SUSY Ward identities, and the generating functions characterize and count amplitudes in the MHV and NMHV sectors. The MHV generating function provides an efficient way to perform the intermediate state helicity sums required to obtain loop amplitudes from trees. The NMHV generating functions rely on the MHV-vertex expansion obtained from recursion relations associated with a 3-line shift of external momenta involving a reference spinor |X]. The recursion relations remain valid for a subset of N = 8 supergravity amplitudes which do not vanish asymptotically for all |X]. The MHV-vertex expansion of the n-graviton NMHV amplitude for n = 5, 6, ..., 11 is independent of |X] and exhibits the asymptotic behavior z n−12 . This presages difficulties for n > 12. Generating functions show how the symmetries of supergravity can be implemented in the quadratic map between supergravity and gauge theory embodied in the KLT and other similar relations between amplitudes in the two theories.

In order to address the issues raised by the recent discovery of non-uniqueness of black holes in five dimensions, we construct a solution of string theory at low energies describing a fivedimensional spinning black ring with three charges that can be interpreted as D1-brane, D5-brane, and momentum charges. The solution possesses closed timelike curves (CTCs) and other pathologies, whose origin we clarify. These pathologies can be avoided by setting any one of the charges, e.g., the momentum, to zero. We argue that the D1-D5-charged black ring, lifted to six dimensions, describes the thermal excitation of a supersymmetric D1-D5 supertube, which is in the same U-duality class as the D0-F1 supertube. We explain how the stringy microscopic description of the D1-D5 system distinguishes between a spherical black hole and a black ring with the same asymptotic charges, and therefore provides a (partial) resolution of the non-uniqueness of black holes in five dimensions.

We find the gravity dual of N = 2 * super-Yang-Mills theory on S 4 and use holography to calculate the universal contribution to the corresponding S 4 free energy at large N and large 't Hooft coupling. Our result matches the expression previously computed using supersymmetric localization in the field theory. This match represents a non-trivial precision test of holography in a non-conformal, Euclidean signature setting.

We study the extension of the approach to the a-theorem of Komargodski and Schwimmer to quantum field theories in d = 6 spacetime dimensions. The dilaton effective action is obtained up to 6th order in derivatives. The anomaly flow a UV − a IR is the coefficient of the 6-derivative Euler anomaly term in this action. It then appears at order p 6 in the low energy limit of npoint scattering amplitudes of the dilaton for n ≥ 4. The detailed structure with the correct anomaly coefficient is confirmed by direct calculation in two examples: (i) the case of explicitly broken conformal symmetry is illustrated by the free massive scalar field, and (ii) the case of spontaneously broken conformal symmetry is demonstrated by the (2,0) theory on the Coulomb branch. In the latter example, the dilaton is a dynamical field so 4-derivative terms in the action also affect n-point amplitudes at order p 6 . The calculation in the (2,0) theory is done by analyzing an M5-brane probe in AdS 7 × S 4 . Given the confirmation in two distinct models, we attempt to use dispersion relations to prove that the anomaly flow is positive in general. Unfortunately the 4-point matrix element of the Euler anomaly is proportional to stu and vanishes for forward scattering. Thus the optical theorem cannot be applied to show positivity. Instead the anomaly flow is given by a dispersion sum rule in which the integrand does not have definite sign. It may be possible to base a proof of the a-theorem on the analyticity and unitarity properties of the 6-point function, but our preliminary study reveals some difficulties.arXiv:1205.3994v1 [hep-th]