New connections between 4D and 5D black holes

Stationary solutions of 5D supergravity with U(1) isometry can be efficiently studied by dimensional reduction to three dimensions, where they reduce to solutions to a locally supersymmetric non-linear sigma model. We generalize this procedure to 5D gauged supergravity, and identify the corresponding gauging in 3D. We pay particular attention to the case where the Killing spinor is non constant along the fibration, which results, even for ungauged supergravity in 5D, in an additional gauging in 3D, without introducing any extra potential. We further study SU(2) × U(1) symmetric solutions, which correspond to geodesic motion on the sigma model (with potential in the gauged case). We identify and study the algebra of BPS constraints relevant for the Breckenridge-Myers-Peet-Vafa black hole, the Gutowski-Reall black hole and several other BPS solutions, and obtain the corresponding radial wave functions in the semi-classical approximation.

Section: Jhep05(2008)045supporting

confidence: 63%

“…Another solution in the same category is the rotating BPS black hole at the tip of a Taub-NUT space [4] 12 with NUT charge L, electric charge µ and angular momentum j…”

Section: Jhep05(2008)045mentioning

confidence: 99%

5D black holes and non-linear sigma models

Berkooz

Pioline

2008

“…weak coupling derivation has been suggested recently using the 4d-5d lift [3,4]. A similar derivation for the more general orbifolds with N = 4 supersymmetry is discussed in [5 -8].…”

Section: Jhep01(2008)023mentioning

confidence: 88%

Comments on the spectrum of CHL dyons

Dabholkar¹,

Gaiotto²,

Nampuri³

2008

Self Cite

105

273

Abstract:We address a number of puzzles relating to the proposed formulae for the degeneracies of dyons in orbifold compactifications of the heterotic string to four dimensions with N = 4 supersymmetry. The partition function for these dyons is given in terms of Siegel modular forms associated with genus-two Riemann surfaces. We point out a subtlety in demonstrating S-duality invariance of the resulting degeneracies and give a prescription that makes the invariance manifest. We show, using M-theory lift of string webs, that the genus-two contribution captures the degeneracy only if a specific irreducibility criterion is satisfied by the charges. Otherwise, in general there can be additional contributions from higher genus Riemann surfaces. We analyze the negative discriminant states predicted by the formula. We show that even though there are no big black holes in supergravity corresponding to these states, there are multi-centered particle-like configurations with subleading entropy in agreement with the microscopic prediction and our prescription for S-duality invariance. The existence of the states is moduli dependent and we exhibit the curves of marginal stability and comment on its relation to S-duality invariance.

“…Starting from ( not very ) recent work in [4] and [32], a considerable interest has been generated in understanding 5D BPS degeneracies by constructing dualities to the better understood 4D sector [20], [23], [33], [34]. Matter of fact, this 4D/5D relation was put forth by [4] as a 5D version of the OSV conjecture [1] …”

Section: Introductionmentioning

confidence: 99%

“…The answer turns out to be in the affirmative; and to do so we shall first reqiure to construct the 4D/5D dictionary for multi-center charges. Compared to the 4D/5D map of [4] for a single black object, the analogous one for multi-centers will turn out a bit more involved again due to the relentless cross-terms. Nevertheless with such a map in hand, transforming amongst 4D/5D multi-center charges, we verify that our fragmented harmonic functions are indeed direct 5D lifts of 4D multi-center solutions.…”

Section: Introductionmentioning

confidence: 99%

More rings to rule them all: fragmentation, 4D↔ 5Dand split-spectral flows

Arsiwalla

2008

In this note we set-up an explicit 5D construction of AdS-fragmentation, whereby a single black ring splits-up into a multi-black ring configuration. Furthermore it is seen that these fragmented rings are equivalent to a direct 5D lift of 4D multicenter black holes. Along the way we also determine the 4D/5D transformations relevant for multi-center charges. It is seen that the physical charges involved in black ring fragmentation are Page charges arising due to 5D Chern-Simons terms.As an application of these methods, we reproduce the total angular momentum of concentric black rings, originally due to Gauntlett and Gutowski. Finally we provide a geometric interpretation of fragmented black rings using the idea of split-spectral flows, which seeks to study charge shifts of a given black ring due to fluxes generated in a multi-ring background.