Henriette Elvang

A Supersymmetric Black Ring

A new supersymmetric black hole solution of five-dimensional supergravity is presented. It has an event horizon of topology S1 x S2. This is the first example of a supersymmetric, asymptotically flat black hole of nonspherical 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.

Supersymmetric black rings and three-charge supertubes

We present supergravity solutions for

Generating Tree Amplitudes in N=4 SYM and N = 8 SG

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Black rings, supertubes, and a stringy resolution of black hole non-uniqueness

-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 nonuniqueness 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.

E7(7) constraints on counterterms in N=8 supergravity

We study n-point tree amplitudes of = 4 super Yang-Mills theory and = 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]. When the shifted amplitude vanishes for large z for all |X], the sum of MHV-vertex diagrams is independent of |X] and gives the correct amplitude. If the shifted amplitude does not vanish for large z, Cauchys theorem includes a term at infinity. Examples show that special choices of |X] eliminate this term and the MHV vertex expansion becomes valid at these values. We show that the MHV-vertex expansion of the n-graviton NMHV amplitude for n = 5,6,...,11 is independent of |X] and exhibits the asymptotic behavior zn−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.

Supersymmetric 4D rotating black holes from 5D black rings

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 five-dimensional 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.

On renormalization group flows and the a-theorem in 6d

Abstract We prove by explicit computation that 6-point matrix elements of D 4 R 4 and D 6 R 4 in N = 8 supergravity have non-vanishing single-soft scalar limits, and therefore these operators violate the continuous E 7 ( 7 ) symmetry. The soft limits precisely match automorphism constraints. Together with previous results for R 4 , this provides a direct proof that no E 7 ( 7 ) -invariant candidate counterterm exists below 7-loop order. At 7-loops, we characterize the infinite tower of independent supersymmetric operators D 4 R 6 , R 8 , φ 2 R 8 , … with n > 4 fields and prove that they all violate E 7 ( 7 ) symmetry. This means that the 4-graviton amplitude determines whether or not the theory is finite at 7-loop order. We show that the corresponding candidate counterterm D 8 R 4 has a non-linear supersymmetrization such that its single- and double-soft scalar limits are compatible with E 7 ( 7 ) up to and including 6-points. At loop orders 7 , 8 , 9 we provide an exhaustive account of all independent candidate counterterms with up to 16 , 14 , 12 fields, respectively, together with their potential single-soft scalar limits.

A charged rotating black ring

We present supersymmetric solutions describing black holes with non-vanishing angular momentum in four dimensional asymptotically flat space. The solutions are obtained by Kaluza-Klein reduction of five-dimensional supersymmetric black rings wrapped on the fiber of a Taub-NUT space. We show that in the four-dimensional description the singularity of the nut can be hidden behind a regular black hole event horizon and thereby obtain an explicit example of a non-static multi-black hole solution in four asymptotically flat dimensions.

Recursion relations, generating functions, and unitarity sums in N = 4 SYM theory

A bstractWe 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 aUV − aIR is the coefficient of the 6-derivative Euler anomaly term in this action. It then appears at order p6 in the low energy limit of n-point 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 p6. The calculation in the (2,0) theory is done by analyzing an M5-brane probe in AdS7 × S4.

Non-supersymmetric black rings as thermally excited supertubes

We construct a supergravity solution describing a charged rotating black ring with S^2xS^1 horizon in a five dimensional asymptotically flat spacetime. In the neutral limit the solution is the rotating black ring recently found by Emparan and Reall. We determine the exact value of the lower bound on J^2/M^3, where J is the angular momentum and M the mass; the black ring saturating this bound has maximum entropy for the given mass. The charged black ring is characterized by mass M, angular momentum J, and electric charge Q, and it also carries local fundamental string charge. The electric charge distributed uniformly along the ring helps support the ring against its gravitational self-attraction, so that J^2/M^3 can be made arbitrarily small while Q/M remains finite. The charged black ring has an extremal limit in which the horizon coincides with the singularity.