A modern fareytail

Manschot, Jan; Moore, Gregory W.

doi:10.4310/cntp.2010.v4.n1.a3

Cited by 103 publications

(146 citation statements)

References 62 publications

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“…One way to achieve this would be to recast the standard type IIA twistorial construction into the manifestly invariant framework developed in [36]. A naive attempt using the standard representation of the MSW elliptic genus as a Poincaré series [42] fails, due to the necessity of regulating the Poincaré series (see appendix C). It is conceivable that this obstruction may be avoided by taking into account the constraints on the polar degeneracies from modular invariance.…”

Section: Jhep04(2013)002mentioning

confidence: 99%

“…One possible strategy would be to recast the type IIA twistorial construction into the manifestly SL(2, Z)-invariant type IIB formalism presented in [36]. As a first step in this direction, one may try to use the Poincaré series representation (also known as Farey tail [41,42]) of the generating functions of the MSW invariants to represent the section of JHEP04(2013)002 (2)) describing D3-instanton corrections at linear order as a sum H = m,n G m,n , such that S-duality acts by permuting these contributions. Unfortunately, this manipulation is formal since Poincaré series with negative weight are divergent without a suitable regularization.…”

Section: Jhep04(2013)002mentioning

confidence: 99%

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D3-instantons, mock theta series and twistors

Alexandrov

Manschot

Pioline

2013

J. High Energ. Phys.

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101

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The D-instanton corrected hypermultiplet moduli space of type II string theory compactified on a Calabi-Yau threefold is known in the type IIA picture to be determined in terms of the generalized Donaldson-Thomas invariants, through a twistorial construction. At the same time, in the mirror type IIB picture, and in the limit where only D3-D1-D(-1)-instanton corrections are retained, it should carry an isometric action of the S-duality group SL(2, Z). We prove that this is the case in the one-instanton approximation, by constructing a holomorphic action of SL(2, Z) on the linearized twistor space. Using the modular invariance of the D4-D2-D0 black hole partition function, we show that the standard Darboux coordinates in twistor space have modular anomalies controlled by period integrals of a Siegel-Narain theta series, which can be canceled by a contact transformation generated by a holomorphic mock theta series.

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Section: Jhep04(2013)002mentioning

confidence: 99%

Section: Jhep04(2013)002mentioning

confidence: 99%

D3-instantons, mock theta series and twistors

Alexandrov

Manschot

Pioline

2013

J. High Energ. Phys.

Self Cite

101

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“…These saddlepoints encode exponentially suppressed contributions to W (q, p) and the full answer thus takes the form of a sum over geometries reminiscent of the black hole Farey tail [50][51][52]. In fact, this sum turns out to be precisely the low-energy manifestation of the so-called Rademacher series, which is a powerful tool to reconstruct the Fourier coefficients of modular objects.…”

Section: Jhep07(2017)094mentioning

confidence: 99%

Mixed Rademacher and BPS black holes

Ferrari

Reys

2017

J. High Energ. Phys.

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Dyonic 1/4-BPS states in Type IIB string theory compactified on K3 × T 2 are counted by meromorphic Jacobi forms. The finite parts of these functions, which are mixed mock Jacobi forms, account for the degeneracy of states stable throughout the moduli space of the compactification. In this paper, we obtain an exact asymptotic expansion for their Fourier coefficients, refining the Hardy-Ramanujan-Littlewood circle method to deal with their mixed-mock character. The result is compared to a low-energy supergravity computation of the exact entropy of extremal dyonic 1/4-BPS single-centered black holes, obtained by applying supersymmetric localization techniques to the quantum entropy function.

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“…This can be understood through the fact that there are no non-vanishing negative weight modular forms at any level. For discussions of this in related contexts, see [12][13][14]. Let us denote by V m the space of possible polar polynomials (without requiring that they correspond to the polar part of a bona fide weak Jacobi form).…”

Section: Modularity Propertiesmentioning

confidence: 99%

Elliptic Genera and 3d Gravity

Benjamin

Cheng

Kachru

et al. 2016

Ann. Henri Poincaré

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Abstract. We describe general constraints on the elliptic genus of a 2d supersymmetric conformal field theory which has a gravity dual with large radius in Planck units. We give examples of theories which do and do not satisfy the bounds we derive, by describing the elliptic genera of symmetric product orbifolds of K3, product manifolds, certain simple families of Calabi-Yau hypersurfaces, and symmetric products of the "Monster CFT". We discuss the distinction between theories with supergravity duals and those whose duals have strings at the scale set by the AdS curvature. Under natural assumptions, we attempt to quantify the fraction of (2,2) supersymmetric conformal theories which admit a weakly curved gravity description, at large central charge.

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A modern fareytail

Cited by 103 publications

References 62 publications

D3-instantons, mock theta series and twistors

D3-instantons, mock theta series and twistors

Mixed Rademacher and BPS black holes

Elliptic Genera and 3d Gravity

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