Person:

Denef, Frederik

Four dimensional N = 2 supergravity has regular, stationary, asymptotically flat BPS solutions with intrinsic angular momentum, describing bound states of separate extremal black holes with mutually nonlocal charges. Though the existence and some properties of these solutions were established some time ago, fully explicit analytic solutions were lacking thus far. In this note, we fill this gap. We show in general that explicit solutions can be constructed whenever an explicit formula is known in the theory at hand for the Bekenstein-Hawking entropy of a single black hole as a function of its charges, and illustrate this with some simple examples. We also give an example of moduli-dependent black hole entropy.

We give an elementary physical derivation of the Kontsevich-Soibelman wall crossing formula, valid for any theory with a 4d N = 2 supergravity description. Our argument leads to a slight generalization of the formula, which relates monodromy to the BPS spectrum.

We initiate a systematic study of the state space of non-extremal, stationary black hole bound states in four-dimensional (N) = 2 supergravity. Specifically, we show that an exponential multitude of classically stable "halo" bound states can be formed between large finite temperature D4-D0 black hole cores and much smaller, arbitrarily charged black holes at the same temperature. We map out in full the regions of existence for thermodynamically stable and metastable bound states in terms of the core's charges and temperature, as well as the region of stability of the core itself. Several features of these systems, such as a macroscopic configurational entropy and exponential relaxation timescales, are similar to those of the extended family of glasses. We draw parallels between the two with a view toward understanding complex systems in fundamental physics.

We investigate degeneracies of BPS states of D-branes on compact Calabi-Yau manifolds. We develop a factorization formula for BPS indices using attractor flow trees associated to multicentered black hole bound states. This enables us to study background dependence of the BPS spectrum, to compute explicitly exact indices of various nontrivial D-brane systems, and to clarify the subtle relation of Donaldson-Thomas invariants to BPS indices of stable D6-D2-D0 states, realized in supergravity as “hole halos.” We introduce a convergent generating function for D4 indices in the large CY volume limit, and prove it can be written as a modular average of its polar part, generalizing the fareytail expansion of the elliptic genus. We show polar states are “split” D6-anti-D6 bound states, and that the partition function factorizes accordingly, leading to a refined version of the OSV conjecture. This differs from the original conjecture in several aspects. In particular we obtain a nontrivial measure factor (g^{−2}{top} e^{−K}) and find factorization requires a cutoff. We show that the main factor determining the cutoff and therefore the error is the existence of “swing states” — D6 states which exist at large radius but do not form stable D6-anti-D6 bound states. We point out a likely breakdown of the OSV conjecture at small (g{top}) (in the large background CY volume limit), due to the surprising phenomenon that for sufficiently large background Kähler moduli, a charge (\Lambda \Gamma) supporting single centered black holes of entropy (\sim \Lambda^2 S(\Gamma)) also admits two-centered BPS black hole realizations whose entropy grows like (\Lambda^3) when (\Lambda \rightarrow \infty).

We examine the recently proposed relations between black hole entropy and the topological string in the context of type II/heterotic string dual models. We consider the degeneracies of perturbative heterotic BPS states. In several examples with N = 4 and N = 2 supersymmetry, we show that the macroscopic degeneracy of small black holes agrees to all orders with the microscopic degeneracy, but misses non-perturbative corrections which are computable in the heterotic dual. Using these examples we refine the previous proposals and comment on their domain of validity as well as on the relevance of helicity supertraces.

We discuss a simple example of an F-theory compactification on a Calabi-Yau fourfold where background fluxes, nonperturbative effects from Euclidean D3 instantons and gauge dynamics on D7 branes allow us to fix all closed and open string moduli. We explicitly check that the known higher order corrections to the potential, which we neglect in our leading approximation, only shift the results by a small amount. In our exploration of the model, we encounter interesting new phenomena, including examples of transitions where D7 branes absorb O3 planes, while changing topology to preserve the net D3 charge.

It has recently been proposed that a class of supersymmetric higher-derivative interactions in Script N = 2 supergravity may encapsulate an infinite number of finite size corrections to the microscopic entropy of certain supersymmetric black holes. If this proposal is correct, it allows one to probe the string theory description of black-hole micro-states to far greater accuracy than has been possible before. We test this proposal for "small" black holes whose microscopic degeneracies can be computed exactly by counting the corresponding perturbative BPS states. We also study the "black hole partition sum" using general properties of of BPS degeneracies. This complements and extends our earlier work in [1].

We provide a qualitative review of flux compactifications of string theory, focusing on broad physical implications and statistical methods of analysis.

The Bekenstein–Hawking entropy of certain black holes can be computed microscopically in string theory by mapping the elusive problem of counting microstates of a strongly gravitating black hole to the tractable problem of counting microstates of a weakly coupled D-brane system, which has no event horizon, and indeed comfortably fits on the head of a pin. We show here that, contrary to widely held beliefs, the entropy of spherically symmetric black holes can easily be dwarfed by that of stationary multi-black-hole “molecules” of the same total charge and energy. Thus, the corresponding pin-sized D-brane systems do not even approximately count the microstates of a single black hole, but rather those of a zoo of entropically dominant multicentered configurations.

We systematically construct the geometries dual to the 1+1 dimensional (0, 4) conformal field theories that arise in the low-energy description of wrapped M5-branes in S¹ × CY₃ compactifications of M-theory. This includes a large number of multicentered black hole bound states asymptotic to AdS₃ × S². In addition, we find many geometries that develop multiple, mutually decoupled AdS₃ × S² throats. We argue there is a useful one to one correspondence between the connected components of the space of solutions and particular limits of type IIA attractor flow trees. We point out that there is a thermodynamic instability of small supersymmetric BTZ black holes to localization on the S², a supersymmetric and exactly solvable analog of the well known AdS-Schwarzschild localization instability, and identify this with the "Entropy Enigma" in four dimensions. We discuss the phase transition this suggests, and initiate the CFT interpretation of these results.