Abstract
We investigate the growth of coefficients in the elliptic genus of symmetric product orbifolds at large central charge. We find that this landscape decomposes into two regions. In one region, the growth of the low energy states is Hagedorn, which indicates a stringy dual. In the other, the growth is much slower, and compatible with the spectrum of a supergravity theory on AdS3. We provide a simple diagnostic which places any symmetric product orbifold in either region. We construct a class of elliptic genera with such supergravity-like growth, indicating the possible existence of new realizations of AdS3/CFT2 where the bulk is a semi-classical supergravity theory. In such cases, we give exact expressions for the BPS degeneracies, which could be matched with the spectrum of perturbative states in a dual supergravity description.
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References
J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys.104 (1986) 207 [INSPIRE].
J.L. Cardy, Operator content of two-dimensional conformally invariant theories, Nucl. phys.B 270 (1986) 186.
A. Strominger, Black hole entropy from near horizon microstates, JHEP02 (1998) 009 [hep-th/9712251] [INSPIRE].
T. Hartman, C.A. Keller and B. Stoica, Universal Spectrum of 2d Conformal Field Theory in the Large c Limit, JHEP09 (2014) 118 [arXiv:1405.5137] [INSPIRE].
N. Benjamin, M.C.N. Cheng, S. Kachru, G.W. Moore and N.M. Paquette, Elliptic Genera and 3d Gravity, Annales Henri Poincaré17 (2016) 2623 [arXiv:1503.04800] [INSPIRE].
A. Belin, J. de Boer, J. Kruthoff, B. Michel, E. Shaghoulian and M. Shyani, Universality of sparse d > 2 conformal field theory at large N , JHEP03 (2017) 067 [arXiv:1610.06186] [INSPIRE].
A. Belin, C.A. Keller and I.G. Zadeh, Genus two partition functions and Rényi entropies of large c conformal field theories, J. Phys.A 50 (2017) 435401 [arXiv:1704.08250] [INSPIRE].
P. Kraus, A. Sivaramakrishnan and R. Snively, Black holes from CFT: Universality of correlators at large c, JHEP08 (2017) 084 [arXiv:1706.00771] [INSPIRE].
E. Mefford, E. Shaghoulian and M. Shyani, Sparseness bounds on local operators in holographic CFTd , JHEP07 (2018) 051 [arXiv:1711.03122] [INSPIRE].
T. Anous, R. Mahajan and E. Shaghoulian, Parity and the modular bootstrap, SciPost Phys.5 (2018) 022 [arXiv:1803.04938] [INSPIRE].
B. Michel, Universality in the OPE Coefficients of Holographic 2d CFTs, arXiv:1908.02873 [INSPIRE].
L.F. Alday and E. Perlmutter, Growing Extra Dimensions in AdS/CFT, JHEP08 (2019) 084 [arXiv:1906.01477] [INSPIRE].
A. Belin, A. Castro, C.A. Keller and B.J. Mühlmann, Siegel Paramodular Forms from Exponential Lifts: Slow versus Fast Growth, arXiv:1910.05353 [INSPIRE].
N. Benjamin, A Refined Count of BPS States in the D1/D5 System, JHEP06 (2017) 028 [arXiv:1610.07607] [INSPIRE].
S. Kachru and A. Tripathy, The Hodge-elliptic genus, spinning BPS states and black holes, Commun. Math. Phys.355 (2017) 245 [arXiv:1609.02158] [INSPIRE].
A. Pakman, L. Rastelli and S.S. Razamat, Diagrams for Symmetric Product Orbifolds, JHEP10 (2009) 034 [arXiv:0905.3448] [INSPIRE].
F.M. Haehl and M. Rangamani, Permutation orbifolds and holography, JHEP03 (2015) 163 [arXiv:1412.2759] [INSPIRE].
A. Belin, C.A. Keller and A. Maloney, String Universality for Permutation Orbifolds, Phys. Rev.D 91 (2015) 106005 [arXiv:1412.7159] [INSPIRE].
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys.38 (1999) 1113 [hep-th/9711200] [INSPIRE].
J.M. Maldacena and A. Strominger, AdS3black holes and a stringy exclusion principle, JHEP12 (1998) 005 [hep-th/9804085] [INSPIRE].
C.A. Keller, Phase transitions in symmetric orbifold CFTs and universality, JHEP03 (2011) 114 [arXiv:1101.4937] [INSPIRE].
N. Seiberg and E. Witten, The D1/D5 system and singular CFT, JHEP04 (1999) 017 [hep-th/9903224] [INSPIRE].
L. Eberhardt, M.R. Gaberdiel and R. Gopakumar, The Worldsheet Dual of the Symmetric Product CFT, JHEP04 (2019) 103 [arXiv:1812.01007] [INSPIRE].
A. Belin, Permutation Orbifolds and Chaos, JHEP11 (2017) 131 [arXiv:1705.08451] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept.323 (2000) 183 [hep-th/9905111] [INSPIRE].
J.R. David, G. Mandal and S.R. Wadia, Microscopic formulation of black holes in string theory, Phys. Rept.369 (2002) 549 [hep-th/0203048] [INSPIRE].
M.R. Gaberdiel, C. Peng and I.G. Zadeh, Higgsing the stringy higher spin symmetry, JHEP10 (2015) 101 [arXiv:1506.02045] [INSPIRE].
C.A. Keller and I.G. Zadeh, Conformal Perturbation Theory for Twisted Fields, arXiv:1907.08207 [INSPIRE].
N. Benjamin, S. Kachru, C.A. Keller and N.M. Paquette, Emergent space-time and the supersymmetric index, JHEP05 (2016) 158 [arXiv:1512.00010] [INSPIRE].
E. Witten, Elliptic Genera and Quantum Field Theory, Commun. Math. Phys.109 (1987) 525 [INSPIRE].
T. Eguchi, H. Ooguri, A. Taormina and S.-K. Yang, Superconformal Algebras and String Compactification on Manifolds with SU(N ) Holonomy, Nucl. Phys.B 315 (1989) 193 [INSPIRE].
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] [INSPIRE].
V. Gritsenko, Elliptic genus of Calabi-Yau manifolds and Jacobi and Siegel modular forms, Alg. Anal.11 (1999) 100 [math/9906190].
S. Datta, L. Eberhardt and M.R. Gaberdiel, Stringy \( \mathcal{N} \) = (2, 2) holography for AdS3, JHEP01 (2018) 146 [arXiv:1709.06393] [INSPIRE].
D. Gepner, Exactly Solvable String Compactifications on Manifolds of SU(N ) Holonomy, Phys. Lett.B 199 (1987) 380 [INSPIRE].
A. Belin, A. Castro, J. Gomes and C.A. Keller, Siegel Modular Forms and Black Hole Entropy, JHEP04 (2017) 057 [arXiv:1611.04588] [INSPIRE].
A. Belin, C.A. Keller and A. Maloney, Permutation Orbifolds in the large N Limit, Annales Henri Poincaŕe (2016) 1 [arXiv:1509.01256] [INSPIRE].
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] [INSPIRE].
J. de Boer, Large N elliptic genus and AdS/CFT correspondence, JHEP05 (1999) 017 [hep-th/9812240] [INSPIRE].
J. de Boer, Six-dimensional supergravity on S3× AdS3and 2-D conformal field theory, Nucl. Phys.B 548 (1999) 139 [hep-th/9806104] [INSPIRE].
P. De Lange, A. Maloney and E. Verlinde, Monstrous Product CFTs in the Grand Canonical Ensemble, arXiv:1807.06200 [INSPIRE].
M.R. Gaberdiel, S. Gukov, C.A. Keller, G.W. Moore and H. Ooguri, Extremal N=(2,2) 2D Conformal Field Theories and Constraints of Modularity, Commun. Num. Theor. Phys.2 (2008) 743 [arXiv:0805.4216] [INSPIRE].
A. Belin, A. Castro, J. Gomes and C.A. Keller, Siegel paramodular forms and sparseness in AdS3/CFT2, JHEP11 (2018) 037 [arXiv:1805.09336] [INSPIRE].
P. Kraus and F. Larsen, Partition functions and elliptic genera from supergravity, JHEP01 (2007) 002 [hep-th/0607138] [INSPIRE].
D.P. Jatkar and A. Sen, Dyon spectrum in CHL models, JHEP04 (2006) 018 [hep-th/0510147] [INSPIRE].
J.R. David and A. Sen, CHL Dyons and Statistical Entropy Function from D1-D5 System, JHEP11 (2006) 072 [hep-th/0605210] [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, JHEP05 (2017) 047 [arXiv:1702.05095] [INSPIRE].
N. Kim, AdS3solutions of IIB supergravity from D3-branes, JHEP01 (2006) 094 [hep-th/0511029] [INSPIRE].
J.P. Gauntlett, O.A.P. Mac Conamhna, T. Mateos and D. Waldram, Supersymmetric AdS3solutions of type IIB supergravity, Phys. Rev. Lett.97 (2006) 171601 [hep-th/0606221] [INSPIRE].
C. Couzens, D. Martelli and S. Schäfer-Nameki, F-theory and AdS3/CFT2(2, 0), JHEP06 (2018) 008 [arXiv:1712.07631] [INSPIRE].
C. Couzens, C. Lawrie, D. Martelli, S. Schäfer-Nameki and J.-M. Wong, F-theory and AdS3/CFT2 , JHEP08 (2017) 043 [arXiv:1705.04679] [INSPIRE].
N.T. Macpherson, Type II solutions on AdS3× S3× S3with large superconformal symmetry, JHEP05 (2019) 089 [arXiv:1812.10172] [INSPIRE].
Y. Lozano, N.T. Macpherson, C. Núñez and A. Ramirez, AdS3solutions in Massive IIA with small \( \mathcal{N} \) = (4, 0) supersymmetry, arXiv:1908.09851 [INSPIRE].
Y. Lozano, N.T. Macpherson, C. Núñez and A. Ramirez, 1/4 BPS AdS3/CFT2, arXiv:1909.09636 [INSPIRE].
Y. Lozano, N.T. Macpherson, C. Núñez and A. Ramirez, Two dimensional \( \mathcal{N} \) = (0, 4) quivers dual to AdS3solutions in massive IIA, arXiv:1909.10510 [INSPIRE].
Y. Lozano, N.T. Macpherson, C. Núñez and A. Ramirez, AdS3solutions in massive IIA, defect CFTs and T-duality, JHEP12 (2019) 013 [arXiv:1909.11669] [INSPIRE].
A. Arabi Ardehali, F. Larsen, J.T. Liu and P. Szepietowski, Quantum corrections to central charges and supersymmetric Casimir energy in AdS3/CFT2, JHEP07 (2019) 071 [arXiv:1811.12367] [INSPIRE].
C. Couzens, H.h. Lam, K. Mayer and S. Vandoren, Black Holes and (0,4) SCFTs from Type IIB on K 3, JHEP08 (2019) 043 [arXiv:1904.05361] [INSPIRE].
M. Eichler and D. Zagier, The Theory of Jacobi Forms (Progress in Mathematics), Birkhäuser, (2013).
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Belin, A., Castro, A., Keller, C.A. et al. The holographic landscape of symmetric product orbifolds. J. High Energ. Phys. 2020, 111 (2020). https://doi.org/10.1007/JHEP01(2020)111
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DOI: https://doi.org/10.1007/JHEP01(2020)111