Abstract
The entropy of generic non-extremal dyonic black holes in the STU model has been shown to admit a remarkably universal form. The missing invariant in the formula was recently identified by Sárosi using the formalism of quantum entanglement as well as a higher dimensional embedding of the U-duality group. Here, we express the non-extremal black hole entropy in the STU model in terms of U-duality covariant tensors. We then provide the extension to the most general non-extremal black hole of ungauged \( \mathcal{N}=8 \) supergravity using E 7(7) invariants. We also conjecture a generalization for ungauged \( \mathcal{N}=2 \) supergravity coupled to vector multiplets with arbitrary cubic prepotential. The most general rotating dyonic black hole solution of the STU model with all scalar moduli turned on is provided in an appendix.
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References
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
J.M. Maldacena, A. Strominger and E. Witten, Black hole entropy in M-theory, JHEP 12 (1997) 002 [hep-th/9711053] [INSPIRE].
N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the simplest quantum field theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [INSPIRE].
E. Cremmer and B. Julia, The N = 8 supergravity theory. I. The Lagrangian, Phys. Lett. B 80 (1978) 48 [INSPIRE].
Z. Bern, J.J. Carrasco, L.J. Dixon, H. Johansson and R. Roiban, The ultraviolet behavior of \( \mathcal{N}=8 \) supergravity at four loops,Phys. Rev. Lett. 103(2009) 081301 [arXiv:0905.2326] [INSPIRE].
L. Susskind, Some speculations about black hole entropy in string theory, hep-th/9309145 [INSPIRE].
G.T. Horowitz and J. Polchinski, A correspondence principle for black holes and strings, Phys. Rev. D 55 (1997) 6189 [hep-th/9612146] [INSPIRE].
D.D.K. Chow and G. Compère, Seed for general rotating non-extremal black holes of \( \mathcal{N}=8 \) supergravity, Class. Quant. Grav. 31 (2014) 022001 [arXiv:1310.1925] [INSPIRE].
D.D.K. Chow and G. Compère, Black holes in \( \mathcal{N}=8 \) supergravity from SO(4, 4) hidden symmetries, Phys. Rev. D 90 (2014) 025029 [arXiv:1404.2602] [INSPIRE].
G. Sárosi, Entropy of non-extremal STU black holes: the F-invariant unveiled, arXiv:1508.06667 [INSPIRE].
E. Cremmer et al., Vector multiplets coupled to N = 2 supergravity: super-Higgs effect, flat potentials and geometric structure, Nucl. Phys. B 250 (1985) 385 [INSPIRE].
M.J. Duff, J.T. Liu and J. Rahmfeld, Four-dimensional string-string-string triality, Nucl. Phys. B 459 (1996) 125 [hep-th/9508094] [INSPIRE].
A. Sen, Black hole solutions in heterotic string theory on a torus, Nucl. Phys. B 440 (1995) 421 [hep-th/9411187] [INSPIRE].
M. Cvetič and C.M. Hull, Black holes and U duality, Nucl. Phys. B 480 (1996) 296 [hep-th/9606193] [INSPIRE].
C.Y. Lee, Invariant polynomials of Weyl groups and applications to the centres of universal enveloping algebras, Can. J. Math. 26 (1974) 583.
F. Berdjis, A criterion for completeness of Casimir operators, J. Math. Phys. 22 (1981) 1851.
F. Berdjis and E. Beslmüller, Casimir operators for F 4 , E 6 , E 7 , and E 8, J. Math. Phys. 22 (1981) 1857.
M. Cvetič and D. Youm, Entropy of nonextreme charged rotating black holes in string theory, Phys. Rev. D 54 (1996) 2612 [hep-th/9603147] [INSPIRE].
E. Cremmer and B. Julia, The SO(8) supergravity, Nucl. Phys. B 159 (1979) 141 [INSPIRE].
M. Günaydin, K. Koepsell and H. Nicolai, Conformal and quasiconformal realizations of exceptional Lie groups, Commun. Math. Phys. 221 (2001) 57 [hep-th/0008063] [INSPIRE].
E. Cremmer, B. Julia, H. Lü and C.N. Pope, Dualization of dualities, Nucl. Phys. B 523 (1998) 73 [hep-th/9710119] [INSPIRE].
A. Ceresole, G. Dall’Agata, S. Ferrara and A. Yeranyan, First order flows for N = 2 extremal black holes and duality invariants, Nucl. Phys. B 824 (2010) 239 [arXiv:0908.1110] [INSPIRE].
D. Kastor and K.Z. Win, Nonextreme Calabi-Yau black holes, Phys. Lett. B 411 (1997) 33 [hep-th/9705090] [INSPIRE].
P. Galli, T. Ortín, J. Perz and C.S. Shahbazi, Non-extremal black holes of N = 2, d = 4 supergravity, JHEP 07 (2011) 041 [arXiv:1105.3311] [INSPIRE].
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ArXiv ePrint: 1510.03582
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Compère, G., Lekeu, V. E 7(7) invariant non-extremal entropy. J. High Energ. Phys. 2016, 95 (2016). https://doi.org/10.1007/JHEP01(2016)095
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DOI: https://doi.org/10.1007/JHEP01(2016)095