A Black Hole Farey Tail

By R. Dijkgraaf, J. Maldacena, G. Moore, Erik P. Verlinde. 2000

335 citations recorded by the source corpus.

We derive an exact expression for the Fourier coefficients of elliptic genera of Calabi-Yau manifolds. When applied to k-fold symmetric products of K3 surfaces the expression is well-suited to studying the AdS/CFT correspondence on AdS3 x S3. The expression also elucidates an SL(2,Z) invariant phase diagram for the D1/D5 system involving deconfining transitions in the limit as k goes to infinity.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/24c56fbbc7f948fbde6602ca9c654b94714d6192

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Citations in the corpus

Microscopic formulation of black holes in string theory (2002, background): “In [191] an elliptic genus calculated from the boundary CFT is interpreted as a sum over this entire SL(2,Z) family of gravitational instantons.”
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”
Multiboundary wormholes and holographic entanglement (2014, background): “ on Bulk Phases and the Mapping Class Group A.1 Mapping Class Group The phase structure of section2.3can be understood a bit more formally as follows. We will begin with the torus case (for which see [65,45,66] for details). The Euclidean geometry is, topologically, a solid donut whose boundary is a”
Averaging over Narain moduli space (2020, background): “(In a supersymmetric extension of three-dimensional gravity, there can be a more clear-cut justification to sum only over handlebodies in evaluating an appropriate index [19].”
The complete superconformal index for N=6 Chern–Simons theory (2009, background): “In AdS3/CFT2, the contribution to the elliptic genus index from BTZ black holes is calculated and further discussed [8].”
Exact and Asymptotic Degeneracies of Small Black Holes (2005, neutral): “For more details and information see [68].”
Quantum Black Holes, Wall Crossing, and Mock Modular Forms (2012, background): “, then our results suggest that mock Jacobi forms would provide the right framework for making the holographic SL(2;Z) symmetry manifest for the indexed partition function considered, for example, in [44, 39, 81]. In the N= 4 case, the mock modularity is closely correlated with the wall-crossing phe”
Chiral gravity, log gravity, and extremal CFT (2009, methodology): “Such sums are known as Poincaré series and first appeared in the context of three dimensional gravity in [52].”
Precision Counting of Small Black Holes (2005, background): “pported in part by the European Research Network MRTN-CT-2004-512194. – 75 – Appendices A. The Rademacher Expansion Here we state brieﬂy the Rademacher expansion. For more details and information see [43]. Suppose we have a “vector-valued nearly holomorphic modular form,” i.e., a collection of funct”
Logarithmic corrections to black hole entropy, from the Cardy formula (2000, background): “A closely related but more general result, obtained from a sophisticated number theoretical analysis that yields a much more complete description of the asymptotics, is discussed in [ 18 ].”
Towards a holographic dual of large- N c QCD (2003, background): “nce we wish to avoid conical singularities in either spacetime at U = UKK,UT, the boundary conditions ﬁx the metric parameters as UKK = 4π 3δτ 2 R3 , U T = 4π δtE 2 R3 . (6.4) 13In analogy with [24], there may be an inﬁnite family of Euclidean solutions labelled by two integers specifying which cy”
Near extremal black hole entropy as entanglement entropy via AdS 2 / CFT 1 (2007, background): “(7)Remember that when the temperature is non-vanishing but is not high enough, the AdS/CFT claims that the dual gravity description is given by the path-integral over infinitely many geometries as in [27, 28].”
Higher spin black holes (2011, background): “An analogous situation occurs when the bulk theory consists of gravity along with pure Chern-Simons gauge fields; the AdS/CFT correspondence has been well developed for that case [39,40].”
Partition functions and elliptic genera from supergravity (2006, methodology): “In keeping with the Farey tail philosophy [9], we will explicitly compute the contribution to the elliptic genus from states below the black hole threshold.”
Split states, entropy enigmas, holes and halos (2007, background): “[26, 27] for the fareytail-transform ẐD4, as well as one for the original ZD4.”
Partition functions of holographic minimal models (2011, background): “Since the higher spin theory also contains standard BTZ black holes, the usual Farey tail picture [63, 64, 65] suggests that CFT states above the black hole threshold might be obtained from the perturbative part of the spectrum upon applying modular transformations.”
Holographic Description of AdS_2 Black Holes (2008, background): “This formula generally applies when 2πRH ≫ c0 24 but, for the CFTs relevant for black holes, we expect it to hold also for 2πRH ∼ c0 24 [33].”
Three-Dimensional Gravity Revisited (2007, result): “Another method to get similar results (expressing black hole degeneracies in terms of coefficients of the singular part of the partition function) is the Farey tail expansion [34].”