Siegel modular forms and black hole entropy

Belin, Alexandre; Castro, Alejandra; Gomes, Jacqueline Ramos de Andrade Antunes; Keller, Christoph A.

doi:10.1007/jhep04(2017)057

Cited by 20 publications

(36 citation statements)

References 61 publications

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“…Are the constraints in this paper a (perhaps roundabout) way to guarantee 'slow growth' ? There has been interesting recent work studying Siegel forms obtained via multiplicative lifts and studying putative (subleading) contributions to macroscopic black hole entropy [77]. It would be educational to extend the analysis of this paper to our generating functions.…”

Section: Discussionmentioning

confidence: 97%

No more walls! A tale of modularity, symmetry, and wall crossing for 1/4 BPS dyons

Paquette

Volpato

Zimet

2017

J. High Energ. Phys.

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Abstract:We determine the generating functions of 1/4 BPS dyons in a class of 4d N = 4 string vacua arising as CHL orbifolds of K3×T 2 , a classification of which has been recently completed. We show that all such generating functions obey some simple physical consistency conditions that are very often sufficient to fix them uniquely. The main constraint we impose is the absence of unphysical walls of marginal stability: discontinuities of 1/4 BPS degeneracies can only occur when 1/4 BPS dyons decay into pairs of 1/2 BPS states. Formally, these generating functions in spacetime can be described as multiplicative lifts of certain supersymmetric indices (twining genera) on the worldsheet of the corresponding nonlinear sigma model on K3. As a consequence, our procedure also leads to an explicit derivation of almost all of these twining genera. The worldsheet indices singled out in this way match precisely a set of functions of interest in moonshine, as predicted by a recent conjecture.

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Section: Discussionmentioning

confidence: 97%

No more walls! A tale of modularity, symmetry, and wall crossing for 1/4 BPS dyons

Paquette

Volpato

Zimet

2017

J. High Energ. Phys.

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“…It is important to check if the more general twining elliptic genera considered in these references admit a 1/4 BPS dyon partition function with integral Fourier coefficients and obey the positivity constraints as expected from black hole physics. Recently multiplicative lifts of more general weak Jacobi forms 6 as well as the the Siegel modular forms of Sp(2, Z) of weight 35 and 12 were studied and were shown to have properties which make them candidates for partition of black holes [32]. It will be interesting to check if the Fourier coefficients of these Siegel modular forms also satisfy the positivity constraints required from black hole physics.…”

Section: Discussionmentioning

confidence: 99%

Dyon degeneracies from Mathieu moonshine symmetry

Chattopadhyaya

David

2017

Phys. Rev. D

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We construct the Siegel modular forms associated with the theta lift of twisted elliptic genera of K3 orbifolded with g corresponding to the conjugacy classes of the Mathieu group M 24 . We complete the construction for all the classes which belong to M 23 ⊂ M 24 and two other classes outside the subgroup M 23 . For this purpose we provide the explicit expressions for all the twisted elliptic genera in all the sectors of these classes. We show that the Siegel modular forms satisfy the required properties for them to be generating functions of 1/4 BPS dyons of type II string theories compactified on K3 × T 2 and orbifolded by g which acts as a Z N automorphism on K3 together with a 1/N shift on a circle of T 2 . In particular the inverse of these Siegel modular forms admit a Fourier expansion with integer coefficients together with the right sign as predicted from black hole physics. Our analysis completes the construction of the partition function for dyons as well as the twisted elliptic genera for all the 7 CHL compactifications.

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“…In previous work [21] we investigated the growth behavior of the Fourier coefficients of such Siegel paramodular forms for heavy states: that is, when writing the coefficients of the reciprocal of the Siegel paramodular form Φ as we define the discriminant of a state as ∆ = 4nm − l 2 . For heavy states with ∆ 1, we showed that c(m, n, l) ≈ e π √ ∆/t .…”

Section: Jhep11(2018)037mentioning

confidence: 99%

Siegel paramodular forms and sparseness in AdS3/CFT2

Belin

Castro

Gomes

et al. 2018

J. High Energ. Phys.

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We discuss the application of Siegel paramodular forms to the counting of polar states in symmetric product orbifold CFTs. We present five special examples and provide exact analytic counting formulas for their polar states. The first example reproduces the known result for type IIB supergravity on AdS 3 ×S 3 ×K3, whereas the other four examples give new counting formulas. Their crucial feature is that the low energy spectrum is very sparse, which suggests the existence of a suitable dual supergravity theory. These examples open a path to novel realizations of AdS 3 /CFT 2 .

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Siegel modular forms and black hole entropy

Cited by 20 publications

References 61 publications

No more walls! A tale of modularity, symmetry, and wall crossing for 1/4 BPS dyons

No more walls! A tale of modularity, symmetry, and wall crossing for 1/4 BPS dyons

Dyon degeneracies from Mathieu moonshine symmetry

Siegel paramodular forms and sparseness in AdS3/CFT2

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