Higher poles and crossing phenomena from twisted genera

Ashok, Sujay K.; Dell’Aquila, Eleonora; Troost, Jan

doi:10.1007/jhep08(2014)087

Cited by 10 publications

(15 citation statements)

References 40 publications

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“…Closely related studies including such a twisting based on a different approach have been given in [7,26].…”

Section: Elliptic Genus With General Spin Structuresmentioning

confidence: 99%

Compact formulas for the completed mock modular forms

Sugawara

2014

J. High Energ. Phys.

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In this paper we present a new compact expression of the elliptic genus of SL(2)/U(1)-supercoset theory by making use of the 'spectral flow method' of the pathintegral evaluation. This new expression is written in a form like a Poincaré series with a non-holomorphic Gaussian damping factor, and manifestly shows the modular and spectral flow properties of a real analytic Jacobi form. As a related problem, we present similar compact formulas for the modular completions of various mock modular forms which appear in the representation theory of N = 2, 4 superconformal algebras.We further discuss the generalization to the cases of arbitrary spin-structures, that is, the world-sheet fermions with twisted boundary conditions parameterized by a continuous parameter. This parameter is naturally identified with the 'u-variable' in the Appell-Lerch sum.

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“…Closely related studies including such a twisting based on a different approach have been given in [7,26].…”

Section: Elliptic Genus With General Spin Structuresmentioning

confidence: 99%

Compact formulas for the completed mock modular forms

Sugawara

2014

J. High Energ. Phys.

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“…Finally, we note that the computation of a Witten index in the presence of a continuous spectrum may yield a result [33][34][35] that is reminiscent of an indefinite theta function. Consider a supersymmetric one-dimensional quantum mechanics model with Hamiltonian H = p 2 + W 2 (x) − ψ † , ψ W ′ (x).…”

Section: Discussionmentioning

confidence: 98%

Indefinite theta functions for counting attractor backgrounds

Cardoso

Cirafici

Nampuri

2014

J. High Energ. Phys.

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In this note, we employ indefinite theta functions to regularize canonical partition functions for single-center dyonic BPS black holes. These partition functions count dyonic degeneracies in the Hilbert space of four-dimensional toroidally compactified heterotic string theory, graded by electric and magnetic charges. The regularization is achieved by viewing the weighted sums of degeneracies as sums over charge excitations in the nearhorizon attractor geometry of an arbitrarily chosen black hole background, and eliminating the unstable modes. This enables us to rewrite these sums in terms of indefinite theta functions. Background independence is then implemented by using the transformation property of indefinite theta functions under elliptic transformations, while modular transformations are used to make contact with semi-classical results in supergravity.

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“…However, while it is holomorphic it is not modular. Based on Zwegers' method [4] and results of Dabholkar et al [5] and Ashok et al [6] we demonstrate how to complete the expressions to give a modular index, which would contribute to the torus partition function. The Appell-Lerch sum of order 2 in the counting function is suggestive of the occurrence of wall-crossing phenomenon due to the dependence of the Fourier expansion on the parameter region.…”

Section: Introductionmentioning

confidence: 84%

“…The result is a holomorphic but not modular expression. In Section 6 we adapt results in [6] to find the modular completion of this index. We comment on the relation to wall-crossing in counting of the BPS states of the M2-M5 system and black hole microstates.…”

Section: Introductionmentioning

confidence: 99%

Mock modular index of M2-M5 brane systems

Okazaki

Smith

2017

Phys. Rev. D

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Publisher's copyright statement:Reprinted with permission from the American Physical Society: Physical Review D 96, 026017 c (2017) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modied, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. We present Bogomolny-Prasad-Sommerfield (BPS) indices of the supergroup Wess-Zumino-Witten (WZW) models that live on intersecting M2-M5-brane systems. They can encode data of the stretched M2-branes between M5-branes and count the BPS states. They are generally expressed in terms of mock theta functions via the Kac-Wakimoto character formula of the affine Lie superalgebra. We give an explicit expression of the index for the PSLð2j2Þ k¼1 WZW model in terms of the second-order multivariable AppellLerch sum. It indicates that wall crossing occurs in the BPS state counting due to the C field on the M5-branes.

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Higher poles and crossing phenomena from twisted genera

Cited by 10 publications

References 40 publications

Compact formulas for the completed mock modular forms

Compact formulas for the completed mock modular forms

Indefinite theta functions for counting attractor backgrounds

Mock modular index of M2-M5 brane systems

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