Abstract
In this paper, we study the conical entropy in string theory in the simplest setup of dividing the nine dimensional space into two halves. This corresponds to the leading quantum correction to the horizon entropy in string theory on the Rindler space. This entropy is also called the conical entropy and includes surface term contributions. We first derive a new simple formula of the conical entropy for any free higher spin fields. Then we apply this formula to computations of conical entropy in open and closed superstring. In our analysis of closed string, we study the twisted conical entropy defined by making use of string theory on Melvin backgrounds. This quantity is easier to calculate owing to the folding trick. Our analysis shows that the conical entropy in closed superstring is UV finite owing to the string scale cutoff.
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References
C. Holzhey, F. Larsen and F. Wilczek, Geometric and renormalized entropy in conformal field theory, Nucl. Phys. B 424 (1994) 443 [hep-th/9403108] [INSPIRE].
P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) P06002 [hep-th/0405152] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
S.N. Solodukhin, Entanglement entropy, conformal invariance and extrinsic geometry, Phys. Lett. B 665 (2008) 305 [arXiv:0802.3117] [INSPIRE].
R.C. Myers and A. Sinha, Holographic c-theorems in arbitrary dimensions, JHEP 01 (2011) 125 [arXiv:1011.5819] [INSPIRE].
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
A. Kitaev and J. Preskill, Topological entanglement entropy, Phys. Rev. Lett. 96 (2006) 110404 [hep-th/0510092] [INSPIRE].
M. Levin and X.G. Wen, Detecting Topological Order in a Ground State Wave Function, Phys. Rev. Lett. 96 (2006) 110405 [cond-mat/0510613].
M. Nozaki, T. Numasawa and T. Takayanagi, Quantum Entanglement of Local Operators in Conformal Field Theories, Phys. Rev. Lett. 112 (2014) 111602 [arXiv:1401.0539] [INSPIRE].
S. He, T. Numasawa, T. Takayanagi and K. Watanabe, Quantum dimension as entanglement entropy in two dimensional conformal field theories, Phys. Rev. D 90 (2014) 041701 [arXiv:1403.0702] [INSPIRE].
P. Caputa, M. Nozaki and T. Takayanagi, Entanglement of local operators in large-N conformal field theories, PTEP 2014 (2014) 093B06 [arXiv:1405.5946] [INSPIRE].
M. Nozaki, Notes on Quantum Entanglement of Local Operators, JHEP 10 (2014) 147 [arXiv:1405.5875] [INSPIRE].
C.T. Asplund, A. Bernamonti, F. Galli and T. Hartman, Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches, JHEP 02 (2015) 171 [arXiv:1410.1392] [INSPIRE].
P. Caputa, J. Simon, A. Stikonas and T. Takayanagi, Quantum Entanglement of Localized Excited States at Finite Temperature, JHEP 01 (2015) 102 [arXiv:1410.2287] [INSPIRE].
M. Srednicki, Entropy and area, Phys. Rev. Lett. 71 (1993) 666 [hep-th/9303048] [INSPIRE].
L. Bombelli, R.K. Koul, J.L. Lee and R.D. Sorkin, A Quantum Source Of Entropy For Black Holes, Phys. Rev. D 34 (1986) 373.
L. Susskind, String theory and the principles of black hole complementarity, Phys. Rev. Lett. 71 (1993) 2367 [hep-th/9307168] [INSPIRE].
L. Susskind, Strings, black holes and Lorentz contraction, Phys. Rev. D 49 (1994) 6606 [hep-th/9308139] [INSPIRE].
L. Susskind, Some speculations about black hole entropy in string theory, hep-th/9309145 [INSPIRE].
L. Susskind and J. Uglum, Black holes, interactions and strings, hep-th/9410074 [INSPIRE].
A. Dabholkar, Quantum corrections to black hole entropy in string theory, Phys. Lett. B 347 (1995) 222 [hep-th/9409158] [INSPIRE].
A. Dabholkar, Strings on a cone and black hole entropy, Nucl. Phys. B 439 (1995) 650 [hep-th/9408098] [INSPIRE].
D.A. Lowe and A. Strominger, Strings near a Rindler or black hole horizon, Phys. Rev. D 51 (1995) 1793 [hep-th/9410215] [INSPIRE].
R. Emparan, Remarks on the Atick-Witten behavior and strings near black hole horizons, hep-th/9412003 [INSPIRE].
A. Adams, J. Polchinski and E. Silverstein, Don’t panic! Closed string tachyons in ALE space-times, JHEP 10 (2001) 029 [hep-th/0108075] [INSPIRE].
A. Dabholkar, Tachyon condensation and black hole entropy, Phys. Rev. Lett. 88 (2002) 091301 [hep-th/0111004] [INSPIRE].
J.A. Harvey, D. Kutasov, E.J. Martinec and G.W. Moore, Localized tachyons and RG flows, hep-th/0111154 [INSPIRE].
J.R. David, M. Gutperle, M. Headrick and S. Minwalla, Closed string tachyon condensation on twisted circles, JHEP 02 (2002) 041 [hep-th/0111212] [INSPIRE].
M. Headrick, S. Minwalla and T. Takayanagi, Closed string tachyon condensation: An Overview, Class. Quant. Grav. 21 (2004) S1539 [hep-th/0405064] [INSPIRE].
D.N. Kabat, Black hole entropy and entropy of entanglement, Nucl. Phys. B 453 (1995) 281 [hep-th/9503016] [INSPIRE].
W. Donnelly and A.C. Wall, Entanglement entropy of electromagnetic edge modes, Phys. Rev. Lett. 114 (2015) 111603 [arXiv:1412.1895] [INSPIRE].
K.-W. Huang, Central Charge and Entangled Gauge Fields, arXiv:1412.2730 [INSPIRE].
D.V. Fursaev and G. Miele, Cones, spins and heat kernels, Nucl. Phys. B 484 (1997) 697 [hep-th/9605153] [INSPIRE].
J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [INSPIRE].
S.N. Solodukhin, Entanglement entropy of black holes, Living Rev. Rel. 14 (2011) 8 [arXiv:1104.3712] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [INSPIRE].
F. Dowker, J.P. Gauntlett, S.B. Giddings and G.T. Horowitz, On pair creation of extremal black holes and Kaluza-Klein monopoles, Phys. Rev. D 50 (1994) 2662 [hep-th/9312172] [INSPIRE].
F. Dowker, J.P. Gauntlett, G.W. Gibbons and G.T. Horowitz, Nucleation of p-branes and fundamental strings, Phys. Rev. D 53 (1996) 7115 [hep-th/9512154] [INSPIRE].
A.A. Tseytlin, Melvin solution in string theory, Phys. Lett. B 346 (1995) 55 [hep-th/9411198] [INSPIRE].
J.G. Russo and A.A. Tseytlin, Exactly solvable string models of curved space-time backgrounds, Nucl. Phys. B 449 (1995) 91 [hep-th/9502038] [INSPIRE].
J.G. Russo and A.A. Tseytlin, Magnetic flux tube models in superstring theory, Nucl. Phys. B 461 (1996) 131 [hep-th/9508068] [INSPIRE].
T. Takayanagi and T. Uesugi, Orbifolds as Melvin geometry, JHEP 12 (2001) 004 [hep-th/0110099] [INSPIRE].
T. Takayanagi and T. Uesugi, D-branes in Melvin background, JHEP 11 (2001) 036 [hep-th/0110200] [INSPIRE].
J. Polchinski, String theory. Vol. 1: An introduction to the bosonic string, Cambridge University Press, Cambridge U.K. (1998).
T. Nishioka and T. Takayanagi, AdS Bubbles, Entropy and Closed String Tachyons, JHEP 01 (2007) 090 [hep-th/0611035] [INSPIRE].
I. Affleck and A.W.W. Ludwig, Universal noninteger ’ground state degeneracy’ in critical quantum systems, Phys. Rev. Lett. 67 (1991) 161 [INSPIRE].
K. Bringmann and L. Rolen, Radial limits of mock theta functions, to appear.
J. Polchinski, Evaluation of the One Loop String Path Integral, Commun. Math. Phys. 104 (1986) 37 [INSPIRE].
K.H. O’Brien and C.I. Tan, Modular Invariance of Thermopartition Function and Global Phase Structure of Heterotic String, Phys. Rev. D 36 (1987) 1184 [INSPIRE].
B. McClain and B.D.B. Roth, Modular Invariance for Interacting Bosonic Strings at Finite Temperature, Commun. Math. Phys. 111 (1987) 539 [INSPIRE].
D. Cvijovic and H.M. Srivastava, Closed-form summations of Dowker’s and related trigonometric sums, J. Phys. A 45 (2012) 374015.
S.N. Solodukhin, Newton constant, contact terms and entropy, Phys. Rev. D 91 (2015) 084028 [arXiv:1502.03758] [INSPIRE].
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He, S., Numasawa, T., Takayanagi, T. et al. Notes on entanglement entropy in string theory. J. High Energ. Phys. 2015, 106 (2015). https://doi.org/10.1007/JHEP05(2015)106
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DOI: https://doi.org/10.1007/JHEP05(2015)106