Abstract
We use continued fractions to perform a systematic and explicit characterization of the decays of two-centred dyonic black holes in 4D \( \mathcal{N} \) = 4 heterotic ℤN CHL models. Thereby we give a new exact solution for the problem of counting decadent dyons in these models.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
R. Dijkgraaf, E.P. Verlinde and H.L. Verlinde, Counting dyons in N = 4 string theory, Nucl. Phys. B 484 (1997) 543 [hep-th/9607026] [INSPIRE].
J.M. Maldacena, G.W. Moore and A. Strominger, Counting BPS black holes in toroidal Type II string theory, hep-th/9903163 [INSPIRE].
S. Chaudhuri, G. Hockney and J.D. Lykken, Maximally supersymmetric string theories in D < 10, Phys. Rev. Lett. 75 (1995) 2264 [hep-th/9505054] [INSPIRE].
S. Chaudhuri and J. Polchinski, Moduli space of CHL strings, Phys. Rev. D 52 (1995) 7168 [hep-th/9506048] [INSPIRE].
J.H. Schwarz and A. Sen, Type IIA dual of the six-dimensional CHL compactification, Phys. Lett. B 357 (1995) 323 [hep-th/9507027] [INSPIRE].
C. Vafa and E. Witten, Dual string pairs with N = 1 and N = 2 supersymmetry in four-dimensions, Nucl. Phys. B Proc. Suppl. 46 (1996) 225 [hep-th/9507050] [INSPIRE].
S. Chaudhuri and D.A. Lowe, Type IIA heterotic duals with maximal supersymmetry, Nucl. Phys. B 459 (1996) 113 [hep-th/9508144] [INSPIRE].
D.P. Jatkar and A. Sen, Dyon spectrum in CHL models, JHEP 04 (2006) 018 [hep-th/0510147] [INSPIRE].
J.R. David, D.P. Jatkar and A. Sen, Product representation of Dyon partition function in CHL models, JHEP 06 (2006) 064 [hep-th/0602254] [INSPIRE].
J.R. David and A. Sen, CHL Dyons and Statistical Entropy Function from D1-D5 System, JHEP 11 (2006) 072 [hep-th/0605210] [INSPIRE].
A. Sen, Walls of Marginal Stability and Dyon Spectrum in N = 4 Supersymmetric String Theories, JHEP 05 (2007) 039 [hep-th/0702141] [INSPIRE].
A. Dabholkar, D. Gaiotto and S. Nampuri, Comments on the spectrum of CHL dyons, JHEP 01 (2008) 023 [hep-th/0702150] [INSPIRE].
M.C.N. Cheng and E. Verlinde, Dying Dyons Don’t Count, JHEP 09 (2007) 070 [arXiv:0706.2363] [INSPIRE].
S. Banerjee, A. Sen and Y.K. Srivastava, Generalities of Quarter BPS Dyon Partition Function and Dyons of Torsion Two, JHEP 05 (2008) 101 [arXiv:0802.0544] [INSPIRE].
A. Dabholkar, K. Narayan and S. Nampuri, Degeneracy of Decadent Dyons, JHEP 03 (2008) 026 [arXiv:0802.0761] [INSPIRE].
S. Banerjee, A. Sen and Y.K. Srivastava, Partition Functions of Torsion > 1 Dyons in Heterotic String Theory on T6, JHEP 05 (2008) 098 [arXiv:0802.1556] [INSPIRE].
A. Dabholkar, J. Gomes and S. Murthy, Counting all dyons in N = 4 string theory, JHEP 05 (2011) 059 [arXiv:0803.2692] [INSPIRE].
M.C.N. Cheng and E.P. Verlinde, Wall Crossing, Discrete Attractor Flow, and Borcherds Algebra, SIGMA 4 (2008) 068 [arXiv:0806.2337] [INSPIRE].
A. Sen, Negative discriminant states in N = 4 supersymmetric string theories, JHEP 10 (2011) 073 [arXiv:1104.1498] [INSPIRE].
A. Dabholkar, S. Murthy and D. Zagier, Quantum Black Holes, Wall Crossing, and Mock Modular Forms, arXiv:1208.4074 [INSPIRE].
F. Ferrari and V. Reys, Mixed Rademacher and BPS Black Holes, JHEP 07 (2017) 094 [arXiv:1702.02755] [INSPIRE].
N.M. Paquette, R. Volpato and M. Zimet, No More Walls! A Tale of Modularity, Symmetry, and Wall Crossing for 1/4 BPS Dyons, JHEP 05 (2017) 047 [arXiv:1702.05095] [INSPIRE].
G. Bossard, C. Cosnier-Horeau and B. Pioline, Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds, SciPost Phys. 7 (2019) 028 [arXiv:1806.03330] [INSPIRE].
A. Chattopadhyaya and J.R. David, Properties of dyons in \( \mathcal{N} \) = 4 theories at small charges, JHEP 05 (2019) 005 [arXiv:1810.12060] [INSPIRE].
A. Chowdhury, A. Kidambi, S. Murthy, V. Reys and T. Wrase, Dyonic black hole degeneracies in \( \mathcal{N} \) = 4 string theory from Dabholkar-Harvey degeneracies, JHEP 10 (2020) 184 [arXiv:1912.06562] [INSPIRE].
F. Fischbach, A. Klemm and C. Nega, Lost Chapters in CHL Black Holes: Untwisted Quarter-BPS Dyons in the ℤ2 Model, JHEP 01 (2021) 157 [arXiv:2005.07712] [INSPIRE].
J.R. David, On walls of marginal stability in N = 2 string theories, JHEP 08 (2009) 054 [arXiv:0905.4115] [INSPIRE].
A. Chowdhury, S. Lal, A. Saha and A. Sen, Black Hole Bound State Metamorphosis, JHEP 05 (2013) 020 [arXiv:1210.4385] [INSPIRE].
A. Sen, Arithmetic of Quantum Entropy Function, JHEP 08 (2009) 068 [arXiv:0903.1477] [INSPIRE].
F. Halter-Koch, Quadratic Irrationals: An Introduction to Classical Number Theory, Chapman and Hall/CRC, (2013).
A. Hatcher, Topology of numbers. Cornell University, (2020), https://pi.math.cornell.edu/~hatcher/TN/TNpage.html.
A. Sen, How Do Black Holes Predict the Sign of the Fourier Coefficients of Siegel Modular Forms?, Gen. Rel. Grav. 43 (2011) 2171 [arXiv:1008.4209] [INSPIRE].
K. Bringmann and K. Ono, The f(q) mock theta function conjecture and partition ranks, Invent. Math. 165 (2006) 243.
K. Bringmann and J. Manschot, From sheaves on P2 to a generalization of the Rademacher expansion, Am. J. MAth. 135 (2013) 1039.
K. Bringmann and K. Ono, Coefficients of Harmonic Maass Forms, Developments in Mathematics (2012), pp. 23–38 [DOI].
K. Bringmann and K. Mahlburg, An extension of the Hardy-Ramanujan circle method and applications to partitions without sequences, Am. J. MAth. 133 (2011) 1151.
K. Bringmann, T. Creutzig and L. Rolen, Negative index Jacobi forms and quantum modular forms, arXiv:1401.7189 [INSPIRE].
D.A. Buell, Binary quadratic forms: classical theory and modern computations, Springer Science & Business Media, (1989).
G.W. Moore, Attractors and arithmetic, hep-th/9807056 [INSPIRE].
G.W. Moore, Arithmetic and attractors, hep-th/9807087 [INSPIRE].
N. Benjamin, S. Kachru, K. Ono and L. Rolen, Black holes and class groups, arXiv:1807.00797 [INSPIRE].
M. Günaydin, S. Kachru and A. Tripathy, Black holes and Bhargava’s invariant theory, J. Phys. A 53 (2020) 444001 [arXiv:1903.02323] [INSPIRE].
N. Banerjee, A. Bhand, S. Dutta, A. Sen and R.K. Singh, Bhargava’s Cube and Black Hole Charges, arXiv:2006.02494 [INSPIRE].
L. Borsten, M.J. Duff and A. Marrani, Black Holes and Higher Composition Laws, arXiv:2006.03574 [INSPIRE].
J.H. Conway, The Sensual Quadratic Form, Mathematical Association of America, (1997).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2007.10302
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Cardoso, G.L., Nampuri, S. & Rosselló, M. Arithmetic of decay walls through continued fractions: a new exact dyon counting solution in \( \mathcal{N} \) = 4 CHL models. J. High Energ. Phys. 2021, 154 (2021). https://doi.org/10.1007/JHEP03(2021)154
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2021)154