Abstract
We analyze the Euclidean geometry near non-extremal NS5-branes in string theory, including regions beyond the horizon and beyond the singularity of the black brane. The various regions have an exact description in string theory, in terms of cigar, trumpet and negative level minimal model conformal field theories. We study the worldsheet elliptic genera of these three superconformal theories, and show that their sum vanishes. We speculate on the significance of this curious sum rule for black hole physics.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. Gibbons and S. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
J.B. Hartle and S.W. Hawking, Path integral derivation of black hole radiance, Phys. Rev. D 13 (1976) 2188 [INSPIRE].
W. Israel, Thermo field dynamics of black holes, Phys. Lett. A 57 (1976) 107 [INSPIRE].
G.T. Horowitz and A. Strominger, Black strings and p-branes, Nucl. Phys. B 360 (1991) 197 [INSPIRE].
S. Elitzur, A. Forge and E. Rabinovici, Some global aspects of string compactifications, Nucl. Phys. B 359 (1991) 581 [INSPIRE].
G. Mandal, A.M. Sengupta and S.R. Wadia, Classical solutions of two-dimensional string theory, Mod. Phys. Lett. A 6 (1991) 1685 [INSPIRE].
E. Witten, On string theory and black holes, Phys. Rev. D 44 (1991) 314 [INSPIRE].
J.M. Maldacena, G.W. Moore and N. Seiberg, Geometrical interpretation of D-branes in gauged WZW models, JHEP 07 (2001) 046 [hep-th/0105038] [INSPIRE].
C. Kounnas, N. Toumbas and J. Troost, A wave-function for stringy universes, JHEP 08 (2007) 018 [arXiv:0704.1996] [INSPIRE].
A. Giveon, M. Porrati and E. Rabinovici, Target space duality in string theory, Phys. Rept. 244 (1994) 77 [hep-th/9401139] [INSPIRE].
J. Troost, The non-compact elliptic genus: mock or modular, JHEP 06 (2010) 104 [arXiv:1004.3649] [INSPIRE].
T. Eguchi and Y. Sugawara, Non-holomorphic modular forms and SL(2, \( \mathbb{R} \))/U(1) superconformal field theory, JHEP 03 (2011) 107 [arXiv:1012.5721] [INSPIRE].
S.K. Ashok and J. Troost, A twisted non-compact elliptic genus, JHEP 03 (2011) 067 [arXiv:1101.1059] [INSPIRE].
E. Witten, On the Landau-Ginzburg description of N = 2 minimal models, Int. J. Mod. Phys. A 9 (1994) 4783 [hep-th/9304026] [INSPIRE].
S.K. Ashok and J. Troost, Elliptic genera of non-compact Gepner models and mirror symmetry, JHEP 07 (2012) 005 [arXiv:1204.3802] [INSPIRE].
P. Di Francesco and S. Yankielowicz, Ramond sector characters and N = 2 Landau-Ginzburg models, Nucl. Phys. B 409 (1993) 186 [hep-th/9305037] [INSPIRE].
H. Ooguri and C. Vafa, Two-dimensional black hole and singularities of CY manifolds, Nucl. Phys. B 463 (1996) 55 [hep-th/9511164] [INSPIRE].
T. Eguchi and Y. Sugawara, SL(2, \( \mathbb{R} \))/U(1) supercoset and elliptic genera of noncompact Calabi-Yau manifolds, JHEP 05 (2004) 014 [hep-th/0403193] [INSPIRE].
Y. Sugawara, ‘Analytic continuation’ of N = 2 minimal model, arXiv:1311.4708 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1311.5189
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Giveon, A., Itzhaki, N. & Troost, J. The black hole interior and a curious sum rule. J. High Energ. Phys. 2014, 63 (2014). https://doi.org/10.1007/JHEP03(2014)063
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2014)063