Abstract
We establish the relation of partition functions of conformal higher spin fields on Weyl equivalent spaces in d = 4 dimension. We express the partition function of Weyl graviton and conformal higher spin fields as an integral over characters on S1 × AdS3, S4, and AdS4. We observe that the partition function of conformal higher spins on hyperbolic cylinders differs from the partition function on S4 by the ‘edge’ contribution. The logarithmic coefficient obtained from the character integral of the partition function of conformal higher spins on AdS4 is the half of that obtained from the partition function on S4. We evaluate the entanglement entropy and the conformal dimension of the twist operator from the partition function on the hyperbolic cylinder. The conformal dimension of the co-dimension two twist operator enables us to find a linear relation between Hofman-Maldacena variables which we use to show the non-unitarity of the theory. We observe that the spectrum of the quasinormal modes of conformal higher spins obtained from the bulk character contains additional distinct states compared to the spectrum of unitary massless higher spin fields.
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G. W. Gibbons and S. W. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
D. Anninos, T. Bautista and B. Mühlmann, The two-sphere partition function in two-dimensional quantum gravity, JHEP 09 (2021) 116 [arXiv:2106.01665] [INSPIRE].
D. Anninos and E. Harris, Three-dimensional de Sitter horizon thermodynamics, JHEP 10 (2021) 091 [arXiv:2106.13832] [INSPIRE].
D. Anninos, D. M. Hofman and S. Vitouladitis, One-dimensional quantum gravity and the Schwarzian theory, JHEP 03 (2022) 121 [arXiv:2112.03793] [INSPIRE].
Z. Sun, AdS one-loop partition functions from bulk and edge characters, JHEP 12 (2021) 064 [arXiv:2010.15826] [INSPIRE].
B. Pethybridge and V. Schaub, Tensors and spinors in de Sitter space, arXiv:2111.14899 [INSPIRE].
M. Grewal and K. Parmentier, Characters, quasinormal modes, and Schwinger pairs in dS2 with flux, JHEP 03 (2022) 165 [arXiv:2112.07630] [INSPIRE].
I. R. Klebanov, S. S. Pufu, S. Sachdev and B. R. Safdi, Rényi entropies for free field theories, JHEP 04 (2012) 074 [arXiv:1111.6290] [INSPIRE].
D. Anninos, F. Denef, Y. T. A. Law and Z. Sun, Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions, JHEP 01 (2022) 088 [arXiv:2009.12464] [INSPIRE].
J. R. David and J. Mukherjee, Partition functions of p-forms from Harish-Chandra characters, JHEP 09 (2021) 094 [arXiv:2105.03662] [INSPIRE].
J. Mukherjee, Partition functions of higher derivative conformal fields on conformally related spaces, JHEP 10 (2021) 236 [arXiv:2108.00929] [INSPIRE].
L.-Y. Hung, R. C. Myers and M. Smolkin, Twist operators in higher dimensions, JHEP 10 (2014) 178 [arXiv:1407.6429] [INSPIRE].
J. F. Donoghue, Quartic propagators, negative norms and the physical spectrum, Phys. Rev. D 96 (2017) 044007 [arXiv:1704.01533] [INSPIRE].
X. O. Camanho and J. D. Edelstein, Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity, JHEP 04 (2010) 007 [arXiv:0911.3160] [INSPIRE].
K.-W. Huang, Central charge and entangled gauge fields, Phys. Rev. D 92 (2015) 025010 [arXiv:1412.2730] [INSPIRE].
H. Osborn and A. C. Petkou, Implications of conformal invariance in field theories for general dimensions, Annals Phys. 231 (1994) 311 [hep-th/9307010] [INSPIRE].
J. R. David and J. Mukherjee, Hyperbolic cylinders and entanglement entropy: gravitons, higher spins, p-forms, JHEP 01 (2021) 202 [arXiv:2005.08402] [INSPIRE].
M. Beccaria, X. Bekaert and A. A. Tseytlin, Partition function of free conformal higher spin theory, JHEP 08 (2014) 113 [arXiv:1406.3542] [INSPIRE].
M. Beccaria and A. A. Tseytlin, CT for conformal higher spin fields from partition function on conically deformed sphere, JHEP 09 (2017) 123 [arXiv:1707.02456] [INSPIRE].
R. Camporesi and A. Higuchi, Spectral functions and zeta functions in hyperbolic spaces, J. Math. Phys. 35 (1994) 4217 [INSPIRE].
R. M. Soni and S. P. Trivedi, Entanglement entropy in (3 + 1)d free U(1) gauge theory, JHEP 02 (2017) 101 [arXiv:1608.00353] [INSPIRE].
S. Giombi, I. R. Klebanov and A. A. Tseytlin, Partition functions and Casimir energies in higher spin AdSd+1/CFTd, Phys. Rev. D 90 (2014) 024048 [arXiv:1402.5396] [INSPIRE].
A. A. Tseytlin, Weyl anomaly of conformal higher spins on six-sphere, Nucl. Phys. B 877 (2013) 632 [arXiv:1310.1795] [INSPIRE].
W. Donnelly and A. C. Wall, Entanglement entropy of electromagnetic edge modes, Phys. Rev. Lett. 114 (2015) 111603 [arXiv:1412.1895] [INSPIRE].
H. Casini and M. Huerta, Entanglement entropy of a Maxwell field on the sphere, Phys. Rev. D 93 (2016) 105031 [arXiv:1512.06182] [INSPIRE].
C. P. Herzog and K.-W. Huang, Boundary conformal field theory and a boundary central charge, JHEP 10 (2017) 189 [arXiv:1707.06224] [INSPIRE].
L. S. Brown and J. P. Cassidy, Stress tensors and their trace anomalies in conformally flat space-times, Phys. Rev. D 16 (1977) 1712 [INSPIRE].
C. P. Herzog and K.-W. Huang, Stress tensors from trace anomalies in conformal field theories, Phys. Rev. D 87 (2013) 081901 [arXiv:1301.5002] [INSPIRE].
D. M. Hofman and J. Maldacena, Conformal collider physics: energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [INSPIRE].
A. Buchel, J. Escobedo, R. C. Myers, M. F. Paulos, A. Sinha and M. Smolkin, Holographic GB gravity in arbitrary dimensions, JHEP 03 (2010) 111 [arXiv:0911.4257] [INSPIRE].
F. Denef, S. A. Hartnoll and S. Sachdev, Black hole determinants and quasinormal modes, Class. Quant. Grav. 27 (2010) 125001 [arXiv:0908.2657] [INSPIRE].
Z. Sun, Higher spin de Sitter quasinormal modes, JHEP 11 (2021) 025 [arXiv:2010.09684] [INSPIRE].
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Mukherjee, J. Partition functions and entanglement entropy: Weyl graviton and conformal higher spin fields. J. High Energ. Phys. 2022, 71 (2022). https://doi.org/10.1007/JHEP04(2022)071
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DOI: https://doi.org/10.1007/JHEP04(2022)071