Abstract
AdS2/CFT1 correspondence predicts that the logarithm of a \( {\mathbb{Z}_N} \) twisted index over states carrying a fixed set of charges grows as 1/N times the entropy of the black hole carrying the same set of charges. In this paper we verify this explicitly by calculating the microscopic \( {\mathbb{Z}_N} \) twisted index for a class of states in the CHL models. This demonstrates that black holes carry more information about the microstates than just the total degeneracy.
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S. Chaudhuri, G. Hockney and J.D. Lykken, Maximally supersymmetric string theories in D < 10, Phys. Rev. Lett. 75 (1995) 2264 [hep-th/9505054] [SPIRES].
S. Chaudhuri and J. Polchinski, Moduli space of CHL strings, Phys. Rev. D 52 (1995) 7168 [hep-th/9506048] [SPIRES].
D.P. Jatkar and A. Sen, Dyon spectrum in CHL models, JHEP 04 (2006) 018 [hep-th/0510147] [SPIRES].
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] [SPIRES];
A. Dabholkar and S. Nampuri, Spectrum of dyons and black holes in CHL orbifolds using borcherds lift, JHEP 11 (2007) 077 [hep-th/0603066] [SPIRES].
J.R. David and A. Sen, CHL dyons and statistical entropy function from D1 − D5 system, JHEP 11 (2006) 072 [hep-th/0605210] [SPIRES].
J.R. David, D.P. Jatkar and A. Sen, Dyon spectrum in N = 4 supersymmetric type-II string theories, JHEP 11 (2006) 073 [hep-th/0607155] [SPIRES].
J.R. David, D.P. Jatkar and A. Sen, Dyon spectrum in generic N = 4 supersymmetric Z(N) orbifolds, JHEP 01 (2007) 016 [hep-th/0609109] [SPIRES].
A. Dabholkar and D. Gaiotto, Spectrum of CHL dyons from genus-two partition function, JHEP 12 (2007) 087 [hep-th/0612011] [SPIRES].
M. Cvetič and D. Youm, Dyonic BPS saturated black holes of heterotic string on a six torus, Phys. Rev. D 53 (1996) 584 [hep-th/9507090] [SPIRES].
M. Cvetič and A.A. Tseytlin, Solitonic strings and BPS saturated dyonic black holes, Phys. Rev. D 53 (1996) 5619 [Erratum ibid. D 55 (1997) 3907] [hep-th/9512031] [SPIRES].
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [SPIRES].
J.C. Breckenridge, R.C. Myers, A.W. Peet and C. Vafa, D-branes and spinning black holes, Phys. Lett. B 391 (1997) 93 [hep-th/9602065] [SPIRES].
B. de Wit, N = 2 electric-magnetic duality in a chiral background, Nucl. Phys. Proc. Suppl. 49 (1996) 191 [hep-th/9602060] [SPIRES].
B. de Wit, N=2 symplectic reparametrizations in a chiral background, Fortsch. Phys. 44 (1996) 529 [hep-th/9603191] [SPIRES].
G. Lopes Cardoso, B. de Wit and T. Mohaupt, Corrections to macroscopic supersymmetric black-hole entropy, Phys. Lett. B 451 (1999) 309 [hep-th/9812082] [SPIRES].
T. Mohaupt, Black hole entropy, special geometry and strings, Fortsch. Phys. 49 (2001) 3 [hep-th/0007195] [SPIRES].
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] [SPIRES].
G. Lopes Cardoso, B. de Wit, J. Kappeli and T. Mohaupt, Asymptotic degeneracy of dyonic N = 4 string states and black hole entropy, JHEP 12 (2004) 075 [hep-th/0412287] [SPIRES].
D. Shih, A. Strominger and X. Yin, Recounting dyons in N = 4 string theory, JHEP 10 (2006) 087 [hep-th/0505094] [SPIRES].
D. Gaiotto, Re-recounting dyons in N = 4 string theory, hep-th/0506249 [SPIRES].
D. Shih and X. Yin, Exact black hole degeneracies and the topological string, JHEP 04 (2006) 034 [hep-th/0508174] [SPIRES].
N. Banerjee, D.P. Jatkar and A. Sen, Adding charges to N = 4 dyons, JHEP 07 (2007) 024 [arXiv:0705.1433] [SPIRES].
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] [SPIRES].
S. Banerjee, A. Sen and Y.K. Srivastava, Partition functions of torsion ¿1 dyons in heterotic string theory on T 6, JHEP 05 (2008) 098 [arXiv:0802.1556] [SPIRES].
A. Dabholkar, J. Gomes and S. Murthy, Counting all dyons in N = 4 string theory, arXiv:0803.2692 [SPIRES].
A. Sen, Quantum entropy function from AdS 2 /CFT 1 correspondence, Int. J. Mod. Phys. A 24 (2009) 4225 [arXiv:0809.3304] [SPIRES].
A. Sen, Arithmetic of quantum entropy function, JHEP 08 (2009) 068 [arXiv:0903.1477] [SPIRES].
A. Sen, A twist in the dyon partition function, JHEP 05 (2010) 028 [arXiv:0911.1563] [SPIRES].
M.G. Alford, J. March-Russell and F. Wilczek, Discrete quantum hair on clack holes and the nonabelian Aharonov-Bohm effect, Nucl. Phys. B 337 (1990) 695 [SPIRES].
S.R. Coleman, J. Preskill and F. Wilczek, Quantum hair on black holes, Nucl. Phys. B 378 (1992) 175 [hep-th/9201059] [SPIRES].
A. Gregori et al., R 2 corrections and non-perturbative dualities of N = 4 string ground states, Nucl. Phys. B 510 (1998) 423 [hep-th/9708062] [SPIRES].
E. Kiritsis, Introduction to non-perturbative string theory, hep-th/9708130 [SPIRES].
N. Banerjee, D.P. Jatkar and A. Sen, Asymptotic expansion of the N = 4 dyon degeneracy, JHEP 05 (2009) 121 [arXiv:0810.3472] [SPIRES].
S. Murthy and B. Pioline, A farey tale for N = 4 dyons, JHEP 09 (2009) 022 [arXiv:0904.4253] [SPIRES].
S. Chaudhuri and D.A. Lowe, Type IIA heterotic duals with maximal supersymmetry, Nucl. Phys. B 459 (1996) 113 [hep-th/9508144] [SPIRES].
P.S. Aspinwall, Some relationships between dualities in string theory, Nucl. Phys. Proc. Suppl. 46 (1996) 30 [hep-th/9508154] [SPIRES].
A. Sen, Walls of marginal stability and dyon spectrum in N = 4 supersymmetric string theories, JHEP 05 (2007) 039 [hep-th/0702141] [SPIRES].
A. Dabholkar, D. Gaiotto and S. Nampuri, Comments on the spectrum of CHL dyons, JHEP 01 (2008) 023 [hep-th/0702150] [SPIRES].
A. Sen, Two centered black holes and N = 4 dyon spectrum, JHEP 09 (2007) 045 [arXiv:0705.3874] [SPIRES].
M.C.N. Cheng and E. Verlinde, Dying dyons don’t count, JHEP 09 (2007) 070 [arXiv:0706.2363] [SPIRES].
A. Sen, Black hole entropy function, attractors and precision counting of microstates, Gen. Rel. Grav. 40 (2008) 2249 [arXiv:0708.1270] [SPIRES].
C.N. Pope, Axial vector anomalies and the index theorem in charged Schwarzschild and Taub-nut spaces, Nucl. Phys. B 141 (1978) 432 [SPIRES].
J.P. Gauntlett, N. Kim, J. Park and P. Yi, Monopole dynamics and BPS dyons in N = 2 super-Yang-Mills theories, Phys. Rev. D 61 (2000) 125012 [hep-th/9912082] [SPIRES].
D. Gaiotto, A. Strominger and X. Yin, New connections between 4D and 5D black holes, JHEP 02 (2006) 024 [hep-th/0503217] [SPIRES].
R. Dijkgraaf, G.W. Moore, E.P. Verlinde and H.L. Verlinde, Elliptic genera of symmetric products and second quantized strings, Commun. Math. Phys. 185 (1997) 197 [hep-th/9608096] [SPIRES].
S. Govindarajan, New Lie algebras from dyonic black holes, talk at NSM 2010, IIT Bombay.
S. Govindarajan, BKM Lie superalgebras from twisted CHL dyons, to appear.
T. Kawai, Y. Yamada and S.-K. Yang, Elliptic genera and N = 2 superconformal field theory, Nucl. Phys. B 414 (1994) 191 [hep-th/9306096] [SPIRES].
L.J. Dixon, V. Kaplunovsky and J. Louis, Moduli dependence of string loop corrections to gauge coupling constants, Nucl. Phys. B 355 (1991) 649 [SPIRES].
T. Kawai, N = 2 heterotic string threshold correction, K3 surface and generalized Kac-Moody superalgebra, Phys. Lett. B 372 (1996) 59 [hep-th/9512046] [SPIRES].
C.D.D. Neumann, The elliptic genus of Calabi-Yau 3-folds and 4-folds, product formulae and generalized Kac-Moody algebras, J. Geom. Phys. 29 (1999) 5 [hep-th/9607029] [SPIRES].
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Sen, A. Discrete information from CHL black holes. J. High Energ. Phys. 2010, 138 (2010). https://doi.org/10.1007/JHEP11(2010)138
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DOI: https://doi.org/10.1007/JHEP11(2010)138