Split states, entropy enigmas, holes and halos

By Frederik Denef, G. Moore. 2007

516 citations recorded by the source corpus.

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 $ g_{\text{top}}^{{ - 2}}{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 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 → ∞.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/134ca5925f59f7e1575d75333d5ac3ea76940c34

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Citations in the corpus

Umbral Moonshine (2012, methodology): “2) via an extension of the program that was initiated in [25]; the antecedents of which include Rademacher’s pioneering work [26] on the elliptic modular invariant J(τ), quantum gravity in three dimensions [27, 28, 29], the AdS/CFT correspondence in physics [30, 31, 32], and the application of Radem”
Witten index and wall crossing (2014, background): “The decay of BPS bound states, which had been known to be due to infinite separation of constituents [15–17, 19], was rephrased by Denef as the run away of the ground state wavefunctions to infinity in the Coulomb branch of the quiver theory [22, 23].”
Quantum black holes, localization, and the topological string (2010, background): “y in an essential way. 3. It has been pointed out that agreement with statistical entropy requires modifying the OSV conjecture by including additional measure factors and nonperturbative corrections [24, 25, 26, 27, 28, 29]. Our localizing solution provides a well-deﬁned starting point to deﬁne the”
Universal spectrum of 2d conformal field theory in the large c limit (2014, background): “These are similar to the enigmatic phases discussed in [28, 29] so we adopt this terminology.”
Quivers, curves, and the tropical vertex (2009, background): “n b a . Moreover, the limit function should be continuous. See [19] for a discussion of results toward the conjecture. A physical context for studying m-Kronecker quivers is explained in Section 4 of [3]. Prediction (iii) ﬁts naturally in the framework of [3]. Acknowledgments Sections 1-3 of the pap”
Framed BPS states (2010, unknown): “Unfortunately, a clear physical derivation of the formula in the supergravity case remains elusive, although, ironically, the semiprimitive wall crossing formula was first derived in the supergravity context [12].”
Spectral Networks (2012, unknown): “Of course, this is not unexpected: it is the wall-crossing phenomenon, and occurs exactly as predicted by the wall-crossing formula [9,3,17,40].”
Dirichlet Branes and Mirror Symmetry (2009, background): “Wall crossing is studied by Denef and Moore from the physical point of view in [111].”
Homological algebra of knots and BPS states (2011, background): “which can be identiﬁed with the set of integers Z. Another feature familiar to the practitionersof the reﬁned / motivic DonaldsonThomas theory is that HBPS can jump as one varies stability conditions [16, 17, 18, 19, 20, 21]. Thus, in a closely related type IIA superstring compactiﬁcation on a Calab”
Quantum Black Holes, Wall Crossing, and Mock Modular Forms (2012, background): “In this case spectral flow is imposed as an additional constraint and follows from gauge invariance under large gauge transformations [22, 33, 43, 23].”
Curve counting via stable pairs in the derived category (2007, background): “o the derived category and made to include the virtual class, our entire discussion here remains conjectural. Similar phenomena have been observed recently in a noncommutative example [49]. The paper [13] also studies counting invariants (and more generally BPS states) and wall crossing in Db(X) fro”
Logarithmic corrections to $${\mathcal{N} = 2}$$ black hole entropy: an infrared window into the microstates (2011, methodology): “1) with [28] indicates that such cancellations might be present, at present we should treat this agreement as accidental.”
Wall-crossing in coupled 2d-4d systems (2011, background): “As in [3], invoking the “halo technique” of [34, 3, 35], the consistency of the wall-crossing of the framed BPS indices implies the wall-crossing formula for the unframed indices μ and ω.”
$\mathcal{N} = 2$ quantum field theories and their BPS quivers (2011, background): “This basic 2-3 decay process is known in various contexts as a primitive decay [4].”
Global structure of five-dimensional fuzzballs (2013, unknown): “These solutions play a very important role in the counting of black-hole entropy at weak coupling using quiver quantum mechanics [31].”
Quantum geometry of refined topological strings (2011, background): “Strictly speaking, this statement is true only with large three-form fluxes turned on [21].”
Wall crossing from Boltzmann black hole halos (2010, background): “This generalizes the semi-primitive wall-crossing formula of [9] which describes the change in the index in the sector with charge γ1 + Nγ2, and some earlier results on higher-rank ADHM and DT invariants [41, 42, 43].”
Refined, Motivic, and Quantum (2009, methodology): “1), has an elegant interpretation in supergravity, if all the charges γi are large [2].”