A Farey Tail for Attractor Black Holes

By J. Boer, Miranda C. N. Cheng, R. Dijkgraaf, J. Manschot, Erik P. Verlinde. 2006

161 citations recorded by the source corpus.

The microstates of 4d BPS black holes in IIA string theory compactified on a Calabi-Yau manifold are counted by a (generalized) elliptic genus of a (0,4) conformal field theory. By exploiting a spectral flow that relates states with different charges, and using the Rademacher formula, we find that the elliptic genus has an exact asymptotic expansion in terms of semi-classical saddle-points of the dual supergravity theory. This generalizes the known "Black Hole Farey Tail" of [1] to the case of attractor black holes.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e3e1b926076fa66808b7de04d8c0ae344bd96f24

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Lectures on black holes, topological strings and quantum attractors (2006, methodology): “More recently, several “derivations” of the weak form of the OSV conjecture have been given, using a M2 − M̄2 or D6− D̄6 representation of the black hole, and some modular properties of the partition function [107, 108, 109, 110].”
Black hole collapse in the 1/c expansion (2016, background): “Early successes include the calculation of black hole entropy [1, 5], thermodynamics [6, 7], and much more.”
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”
Quantum Black Holes, Wall Crossing, and Mock Modular Forms (2012, methodology): “mework the modular symmetry is identied with the SL(2;Z) mapping class group of the boundary torus [78], whereas the elliptic symmetry is identied with large gauge transformations of the 3-form eld [39] as we have already discussed in x11.1. We now describe how the quarter-BPS black holes considered”
Topological String Theory on Compact Calabi–Yau: Modularity and Boundary Conditions (2006, methodology): “s 20 and for all other the results up genus 12 are available at [62]. 39 it was suggested to ﬁx a very similar ambiguity to a anholomorphic SL(2,Z)-modular elliptic index of a D4− D2− D0 brane system [66, 67, 68]. There one uses SL(2,Z) invariance of the index and a dual dilute gas approximation in ”
Black hole bound states in AdS(3) x S**2 (2008, methodology): “which are obtained from the original ones by subtracting out the contributions of the zero modes of the additional currents, so only the oscillator contributions remain. In our case they are given by [41]: L0 0 c 24 = (L0 0)cyl = q^0 := (q0 1 2 DABq Aq B); L~0 0 c 24 = (L~0 0)cyl = 0: (3.57) These r”
Dying dyons don't count (2007, background): “ = 2 (recall that c(n) = 0 for n< 1), and vice versa. This suggests that there might be a way of rewriting the generating function analogous to the sum over modular images of the polar terms as in [20, 21, 22, 14]. We hope to put these puzzles together and return to these issues in the future. An”