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Title: Correction of Cardy–Verlinde formula for Fermions and Bosons with modified dispersion relation

Abstract

Cardy–Verlinde formula links the entropy of conformal symmetry field to the total energy and its Casimir energy in a D-dimensional space. To correct black hole thermodynamics, modified dispersion relation can be used which is proposed as a general feature of quantum gravity approaches. In this paper, the thermodynamics of Schwarzschild four-dimensional black hole is corrected using the modified dispersion relation for Fermions and Bosons. Finally, using modified thermodynamics of Schwarzschild four-dimensional black hole, generalization for Cardy–Verlinde formula is obtained. - Highlights: • The modified Cardy–Verlinde formula obtained using MDR for Fermions and Bosons. • The modified entropy of the black hole used to correct the Cardy–Verlinde formula. • The modified entropy of the CFT has been obtained.

Authors:
;
Publication Date:
OSTI Identifier:
22617501
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 380; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BLACK HOLES; BOSONS; CONFORMAL INVARIANCE; DISPERSION RELATIONS; ENTROPY; FERMIONS; FOUR-DIMENSIONAL CALCULATIONS; QUANTUM GRAVITY; SYMMETRY BREAKING; THERMODYNAMICS

Citation Formats

Sadatian, S. Davood, E-mail: sd-sadatian@um.ac.ir, and Dareyni, H. Correction of Cardy–Verlinde formula for Fermions and Bosons with modified dispersion relation. United States: N. p., 2017. Web. doi:10.1016/J.AOP.2017.03.009.
Sadatian, S. Davood, E-mail: sd-sadatian@um.ac.ir, & Dareyni, H. Correction of Cardy–Verlinde formula for Fermions and Bosons with modified dispersion relation. United States. doi:10.1016/J.AOP.2017.03.009.
Sadatian, S. Davood, E-mail: sd-sadatian@um.ac.ir, and Dareyni, H. Mon . "Correction of Cardy–Verlinde formula for Fermions and Bosons with modified dispersion relation". United States. doi:10.1016/J.AOP.2017.03.009.
@article{osti_22617501,
title = {Correction of Cardy–Verlinde formula for Fermions and Bosons with modified dispersion relation},
author = {Sadatian, S. Davood, E-mail: sd-sadatian@um.ac.ir and Dareyni, H.},
abstractNote = {Cardy–Verlinde formula links the entropy of conformal symmetry field to the total energy and its Casimir energy in a D-dimensional space. To correct black hole thermodynamics, modified dispersion relation can be used which is proposed as a general feature of quantum gravity approaches. In this paper, the thermodynamics of Schwarzschild four-dimensional black hole is corrected using the modified dispersion relation for Fermions and Bosons. Finally, using modified thermodynamics of Schwarzschild four-dimensional black hole, generalization for Cardy–Verlinde formula is obtained. - Highlights: • The modified Cardy–Verlinde formula obtained using MDR for Fermions and Bosons. • The modified entropy of the black hole used to correct the Cardy–Verlinde formula. • The modified entropy of the CFT has been obtained.},
doi = {10.1016/J.AOP.2017.03.009},
journal = {Annals of Physics},
number = ,
volume = 380,
place = {United States},
year = {Mon May 15 00:00:00 EDT 2017},
month = {Mon May 15 00:00:00 EDT 2017}
}
  • In a recent paper by E. Verlinde, hep-th/0008140, an interesting formula has been put forward, which relates the entropy of a conformal formal field in arbitrary dimensions to its total energy and Casimir energy. This formula has been shown to hold for the conformal field theories that have anti{endash}de Sitter (AdS) duals in the cases of AdS Schwarzschild black holes and AdS Kerr black holes. In this paper we further check this formula with various black holes with AdS asymptotics. For the hyperbolic AdS black holes, the Cardy-Verlinde formula is found to hold if we choose the ''massless'' black holemore » as the ground state, but in this case, the Casimir energy is negative. For the AdS Reissner-Nordstro''m black holes in arbitrary dimensions and charged black holes in D=5, D=4, and D=7 maximally supersymmetric gauged supergravities, the Cardy-Verlinde formula holds as well, but a proper internal energy, which corresponds to the mass of supersymmetric backgrounds, must be subtracted from the total energy. We fail to rewrite the entropy of corresponding conformal field theories in terms of the Cardy-Verlinde formula for the AdS black holes in Lovelock gravity.« less
  • In this Letter, we compute the corrections to the Cardy-Verlinde formula of the d-dimensional Schwarzschild black hole. These corrections stem from the generalized uncertainty principle. Then we show one can take into account the generalized uncertainty principle corrections of the Cardy-Verlinde entropy formula by just redefining the Virasoro operator L{sub 0} and the central charge c.
  • We study the AdS rotating black hole solution for the Bergshoeff-Hohm-Townsend massive gravity in three dimensions. The field equations of the asymptotically AdS black hole of the static metric can be expressed as the first law of thermodynamics, i.e. dE=TdS-PdV. The corrected Hawking-like temperature and entropy of the asymptotically AdS rotating black hole are calculated using the Cardy formula and the tunneling method. Comparison of these methods will help identify the unknown leading correction parameter {beta}{sub 1} in the tunneling method.
  • We review and extend evidence for the validity of a generalized Verlinde formula, in particular, nonrational conformal field theories. We identify a subset of representations of the chiral algebra in nonrational conformal field theories that give rise to an analogue of the relation between modular S-matrices and fusion coefficients in rational conformal field theories. To that end we review and extend the Cardy-type brane calculations in bosonic and supersymmetric Liouville theory (and its duals) as well as in H{sub 3}{sup +}. We analyze the three-point functions of Liouville theory and of H{sub 3}{sup +} in detail to directly identify themore » fusion coefficients from the operator product expansion. Moreover, we check the validity of a proposed generic formula for localized brane one-point functions in nonrational conformal field theories.« less
  • We have recently developed methods for obtaining exact two-point resistance of the complete graph minus N edges. We use these methods to obtain closed formulas of certain trigonometrical sums that arise in connection with one-dimensional lattice, in proving Scott’s conjecture on permanent of Cauchy matrix, and in the perturbative chiral Potts model. The generalized trigonometrical sums of the chiral Potts model are shown to satisfy recursion formulas that are transparent and direct, and differ from those of Gervois and Mehta. By making a change of variables in these recursion formulas, the dimension of the space of conformal blocks of SU(2)more » and SO(3) WZW models may be computed recursively. Our methods are then extended to compute the corner-to-corner resistance, and the Kirchhoff index of the first non-trivial two-dimensional resistor network, 2×N. Finally, we obtain new closed formulas for variant of trigonometrical sums, some of which appear in connection with number theory. -- Highlights: • Alternative derivation of certain trigonometrical sums of the chiral Potts model are given. • Generalization of these trigonometrical sums satisfy recursion formulas. • The dimension of the space of conformal blocks may be computed from these recursions. • Exact corner-to-corner resistance, the Kirchhoff index of 2×N are given.« less