Frederik Denef

Split states, entropy enigmas, holes and halos

A bstractWe 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

Supergravity Flows and D-brane Stability

g_{\text{top}}^{{ - 2}}{e^{{ - K}}}

Distributions of flux vacua

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 gtop (in the large background CY volume limit), due to the surprising phenomenon that for sufficiently large background Kähler moduli, a charge Λ Γ supporting single centered black holes of entropy ~ Λ2S(Γ) also admits two-centered BPS black hole realizations whose entropy grows like Λ3 when Λ → ∞.

Building a better racetrack

We investigate the correspondence between existence/stability of BPS states in type-II string theory compactified on a Calabi-Yau manifold and BPS solutions of four-dimensional N = 2 supergravity. Some paradoxes emerge, and we propose a resolution by considering composite configurations. This in turn gives a smooth effective field theory description of decay at marginal stability. We also discuss the connection with 3-pronged strings, the Joyce transition of special lagrangian submanifolds, and Π-stability.

Quantum quivers and Hall / hole halos

We give results for the distribution and number of flux vacua of various types, supersymmetric and nonsupersymmetric, in IIB string theory compactified on Calabi-Yau manifolds. We compare this with related problems such as counting attractor points.

Exact solutions for supersymmetric stationary black hole composites

We find IIb compactifications on Calabi-Yau orientifolds in which all Kahler moduli are stabilized, along lines suggested by Kachru, Kallosh, Linde and Trivedi.

Distributions of Nonsupersymmetric Flux Vacua

Two pictures of BPS bound states in Calabi-Yau compactifications of type II string theory exist, one as a set of particles at equilibrium separations from each other, the other as a fusion of D-branes at a single point of space. We show how quiver quantum mechanics smoothly interpolates between the two, and use this, together with recent mathematical results on the cohomology of quiver varieties, to solve some nontrivial ground state counting problems in multi-particle quantum mechanics, including one arising in the setup of the spherical quantum Hall effect, and to count ground state degeneracies of certain dyons in supersymmetric Yang-Mills theories. A crucial ingredient is a non-renormalization theorem in N = 4 quantum mechanics for the first order part of the Lagrangian in an expansion in powers of velocity.

Exact and asymptotic degeneracies of small black holes

A bstractFour dimensional

Split Attractor Flows and the Spectrum of BPS D-branes on the Quintic

\mathcal{N} = {2}

Physics of String Flux Compactifications

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.