Abstract
W N,k minimal models possess an interesting class of ‘light’ primaries which control much of the low energy density of states in the large N ’t Hooft limit. In this paper we conduct a detailed exploration of their distribution using a combination of numerical and analytical techniques. We also make some observations about the density of states of the full CFT. Our results appear to support the contention that there is no finite temperature analogue of the Hawking-Page transition in these systems.
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M.R. Gaberdiel and R. Gopakumar, Minimal Model Holography, J. Phys. A 46 (2013) 214002 [arXiv:1207.6697] [INSPIRE].
S. Giombi and X. Yin, The Higher Spin/Vector Model Duality, J. Phys. A 46 (2013) 214003 [arXiv:1208.4036] [INSPIRE].
M. Ammon, M. Gutperle, P. Kraus and E. Perlmutter, Black holes in three dimensional higher spin gravity: A review, J. Phys. A 46 (2013) 214001 [arXiv:1208.5182] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, An AdS 3 Dual for Minimal Model CFTs, Phys. Rev. D 83 (2011) 066007 [arXiv:1011.2986] [INSPIRE].
S. Prokushkin and M.A. Vasiliev, Higher spin gauge interactions for massive matter fields in 3-D AdS space-time, Nucl. Phys. B 545 (1999) 385 [hep-th/9806236] [INSPIRE].
S. Prokushkin and M.A. Vasiliev, 3-d higher spin gauge theories with matter, hep-th/9812242 [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Triality in Minimal Model Holography, JHEP 07 (2012) 127 [arXiv:1205.2472] [INSPIRE].
M.R. Gaberdiel, R. Gopakumar, T. Hartman and S. Raju, Partition Functions of Holographic Minimal Models, JHEP 08 (2011) 077 [arXiv:1106.1897] [INSPIRE].
P. Kraus and E. Perlmutter, Partition functions of higher spin black holes and their CFT duals, JHEP 11 (2011) 061 [arXiv:1108.2567] [INSPIRE].
M.R. Gaberdiel, T. Hartman and K. Jin, Higher Spin Black Holes from CFT, JHEP 04 (2012) 103 [arXiv:1203.0015] [INSPIRE].
C.-M. Chang and X. Yin, Higher Spin Gravity with Matter in AdS 3 and Its CFT Dual, JHEP 10 (2012) 024 [arXiv:1106.2580] [INSPIRE].
C. Ahn, The Coset Spin-4 Casimir Operator and Its Three-Point Functions with Scalars, JHEP 02 (2012) 027 [arXiv:1111.0091] [INSPIRE].
M. Ammon, P. Kraus and E. Perlmutter, Scalar fields and three-point functions in D = 3 higher spin gravity, JHEP 07 (2012) 113 [arXiv:1111.3926] [INSPIRE].
C.-M. Chang and X. Yin, Correlators in W N Minimal Model Revisited, JHEP 10 (2012) 050 [arXiv:1112.5459] [INSPIRE].
E. Hijano, P. Kraus and E. Perlmutter, Matching four-point functions in higher spin AdS 3 /CF T 2, JHEP 05 (2013) 163 [arXiv:1302.6113] [INSPIRE].
S. Giombi and I.R. Klebanov, One Loop Tests of Higher Spin AdS/CFT, arXiv:1308.2337 [INSPIRE].
K. Papadodimas and S. Raju, Correlation Functions in Holographic Minimal Models, Nucl. Phys. B 856 (2012) 607 [arXiv:1108.3077] [INSPIRE].
A. Castro, R. Gopakumar, M. Gutperle and J. Raeymaekers, Conical Defects in Higher Spin Theories, JHEP 02 (2012) 096 [arXiv:1111.3381] [INSPIRE].
E. Perlmutter, T. Prochazka and J. Raeymaekers, The semiclassical limit of W N CFTs and Vasiliev theory, JHEP 05 (2013) 007 [arXiv:1210.8452] [INSPIRE].
A. Campoleoni and S. Fredenhagen, On the higher-spin charges of conical defects, Phys. Lett. B 726 (2013) 387 [arXiv:1307.3745] [INSPIRE].
A. Campoleoni, T. Prochazka and J. Raeymaekers, A note on conical solutions in 3D Vasiliev theory, JHEP 05 (2013) 052 [arXiv:1303.0880] [INSPIRE].
C.-M. Chang and X. Yin, A semi-local holographic minimal model, Phys. Rev. D 88 (2013) 106002 [arXiv:1302.4420] [INSPIRE].
A. Jevicki and J. Yoon, Field Theory of Primaries in W N Minimal Models, JHEP 11 (2013) 060 [arXiv:1302.3851] [INSPIRE].
S.H. Shenker and X. Yin, Vector Models in the Singlet Sector at Finite Temperature, arXiv:1109.3519 [INSPIRE].
S. Banerjee et al., Smoothed Transitions in Higher Spin AdS Gravity, Class. Quant. Grav. 30 (2013) 104001 [arXiv:1209.5396] [INSPIRE].
D. Berenstein, A toy model for the AdS/CFT correspondence, JHEP 07 (2004) 018 [hep-th/0403110] [INSPIRE].
H. Lin, O. Lunin and J.M. Maldacena, Bubbling AdS space and 1/2 BPS geometries, JHEP 10 (2004) 025 [hep-th/0409174] [INSPIRE].
M.R. Gaberdiel and P. Suchanek, Limits of Minimal Models and Continuous Orbifolds, JHEP 03 (2012) 104 [arXiv:1112.1708] [INSPIRE].
A.M. Vershik, Statistical mechanics of combinatorial partitions, and their limit shapes, Funct. Anal. Appl. 30 (1996) 90.
A.M. Vershik and D.A. Pavlov, Numerical experiments in the problems of asymptotic representation theory, Zapiski Nauchnykh Seminarov POMI 373 (2009) 77.
S.G. Naculich and H.J. Schnitzer, Duality Between SU(N )k and SU(K)N WZW Models, Nucl. Phys. B 347 (1990) 687 [INSPIRE].
J. de Boer and M. Shigemori, Exotic Branes in String Theory, Phys. Rept. 532 (2013) 65 [arXiv:1209.6056] [INSPIRE].
J. Lucietti and M. Rangamani, Asymptotic counting of BPS operators in superconformal field theories, J. Math. Phys. 49 (2008) 082301 [arXiv:0802.3015] [INSPIRE].
N.W. Ashcroft and N.D. Mermin, Solid State Physics, Rinehart and Winston, New York U.S.A. (1976).
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Gaberdiel, M.R., Gopakumar, R. & Rangamani, M. The spectrum of light states in large N minimal models. J. High Energ. Phys. 2014, 116 (2014). https://doi.org/10.1007/JHEP01(2014)116
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DOI: https://doi.org/10.1007/JHEP01(2014)116