Abstract
We provide a holographic interpretation of a class of three-dimensional wormhole spacetimes. These spacetimes have multiple asymptotic regions which are separated from each other by horizons. Each such region is isometric to the BTZ black hole and there is non-trivial spacetime topology hidden behind the horizons. We show that application of the real-time gauge/gravity duality results in a complete holographic description of these spacetimes with the dual state capturing the non-trivial topology behind the horizons. We also show that these spacetimes are in correspondence with trivalent graphs and provide an explicit metric description with all physical parameters appearing in the metric.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Maldacena J.M.: The large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2, 231–252 (1998)
Gubser S.S., Klebanov I.R., Polyakov A.M.: Gauge theory correlators from non-critical string theory. Phys. Lett. B 428, 105–114 (1998)
Witten E.: Anti-de Sitter space and holography. Adv. Theor. Math. Phys. 2, 253–291 (1998)
Skenderis K., van Rees B.C.: Real-time gauge/gravity duality. Phys. Rev. Lett. 101, 081601 (2008)
Skenderis, K., van Rees, B.C.: Real-time gauge/gravity duality: Prescription, Renormalization and Examples. http://arxiv.org/abs/0812.2909v2 [hep-th], 2009
Schwinger J.S.: Brownian motion of a quantum oscillator. J. Math. Phys. 2, 407–432 (1961)
Bakshi P.M., Mahanthappa K.T.: Expectation value formalism in quantum field theory. 1. J. Math. Phys. 4, 1–11 (1963)
Bakshi P.M., Mahanthappa K.T.: Expectation value formalism in quantum field theory. 2. J. Math. Phys. 4, 12–16 (1963)
Keldysh L.V.: Diagram technique for nonequilibrium processes. Zh. Eksp. Teor. Fiz. 47, 1515–1527 (1964) [Sov. Phys. JETP 20, 1018 (1965)]
Hartle J.B., Hawking S.W.: Wave Function of the Universe. Phys. Rev. D 28, 2960–2975 (1983)
Maldacena J.M.: Eternal black holes in Anti-de-Sitter.. JHEP 04, 021 (2003)
Aminneborg S., Bengtsson I., Brill D., Holst S., Peldan P.: Black holes and wormholes in 2+1 dimensions. Class. Quant. Grav. 15, 627–644 (1998)
Brill, D.: Black holes and wormholes in 2+1 dimensions. http://arxiv.org/abs/gr-qc/9904083v2, 1999
Skenderis K., Solodukhin S.N.: Quantum effective action from the AdS/CFT correspondence. Phys. Lett. B 472, 316–322 (2000)
Krasnov K.: Holography and Riemann surfaces. Adv. Theor. Math. Phys. 4, 929–979 (2000)
Henningson M., Skenderis K.: Holography and the Weyl anomaly. Fortsch. Phys. 48, 125–128 (2000)
Henningson M., Skenderis K.: The holographic Weyl anomaly. JHEP 07, 023 (1998)
de Haro S., Solodukhin S.N., Skenderis K.: Holographic reconstruction of spacetime and renormalization in the AdS/CFT correspondence. Commun. Math. Phys. 217, 595–622 (2001)
Skenderis K.: Asymptotically Anti-de Sitter spacetimes and their stress energy tensor. Int. J. Mod. Phys. A 16, 740–749 (2001)
Banados M., Teitelboim C., Zanelli J.: The Black hole in three-dimensional space-time. Phys. Rev. Lett. 69, 1849–1851 (1992)
Banados M., Henneaux M., Teitelboim C., Zanelli J.: Geometry of the (2+1) black hole. Phys. Rev. D 48, 1506–1525 (1993)
Barbot T.: Causal properties of AdS-isometry groups. I: Causal actions and limit sets. Adv. Theor. Math. Phys. 12, 1–66 (2008)
Barbot, T.: Causal properties of AdS-isometry groups. II: BTZ multi black-holes. http://arxiv.org/abs/math.gt/0510065v2 [math, GT], 2006
van Rees, B.: Worm holes in 2+1 dimensions. Master’s thesis, http://staff.science.uva.nl/~brees/report/report.pdf June, 2006
Imayoshi, Y., Taniguchi, M.: An Introduction to Teichmnüller Spaces. Berlin-Heidelberg Newyork: Springer-Verlag, 1992
Lehto O.: Univalent Functions and Teichmüller Spaces. Springer-Verlag, Berlin-Heidelberg Newyork (1986)
Nag S.: The Complex Analytic Theory of Teichmüller spaces. Newyork, John Wiley & Sons (1988)
Galloway G.J., Schleich K., Witt D.M., Woolgar E.: Topological Censorship and Higher Genus Black Holes. Phys. Rev. D60, 104039 (1999)
Carlip S., Teitelboim C.: Aspects of black hole quantum mechanics and thermodynamics in (2+1)-dimensions. Phys. Rev. D51, 622–631 (1995)
Krasnov K.: On holomorphic factorization in asymptotically AdS 3D gravity. Class. Quant. Grav. 20, 4015–4042 (2003)
Krasnov K.: Black Hole Thermodynamics and Riemann Surfaces. Class. Quant. Grav. 20, 2235–2250 (2003)
Takhtajan L., Zograf P.: On uniformization of Riemann surfaces and the Weyl-Peterson metric on Teichmuller and Schottky spaces. Math. USSR Sbornik 60, 297–313 (1988)
Imbimbo C., Schwimmer A., Theisen S., Yankielowicz S.: Diffeomorphisms and holographic anomalies. Class. Quant. Grav. 17, 1129–1138 (2000)
Maldacena J.M., Maoz L.: Wormholes in AdS. JHEP 02, 053 (2004)
Parlier H.: Fixed point free involutions on Riemann surfaces. Israel J. Math. 166, 297–311 (2008)
Anderson, M.T.: Geometric aspects of the AdS/CFT correspondence. http://arxiv.org/abs/hep-th/0403087v2, 2004
Papadimitriou I., Skenderis K.: Thermodynamics of asymptotically locally AdS spacetimes. JHEP 08, 004 (2005)
Freivogel B. et al.: Inflation in AdS/CFT. JHEP 03, 007 (2006)
Louko J., Marolf D.: Single-exterior black holes and the AdS-CFT conjecture. Phys. Rev. D59, 066002 (1999)
Hawking S.W., Page D.N.: Thermodynamics of black holes in anti-de Sitter space. Commun. Math. Phys. 87, 577 (1983)
Maldacena J.M., Strominger A.: AdS(3) black holes and a stringy exclusion principle. JHEP 12, 005 (1998)
Yin, X.: Partition Functions of Three-Dimensional Pure Gravity. http://arxiv.org/abs/0710.2129v2 [hep-th] (2008)
Aminneborg S., Bengtsson I., Holst S.: A spinning Anti-de Sitter wormhole. Class. Quant. Grav. 16, 363–382 (1999)
Brill D.: 2+1-dimensional black holes with momentum and angular momentum. Annalen Phys. 9, 217–226 (2000)
Krasnov K.: Analytic continuation for asymptotically AdS 3D gravity. Class. Quant. Grav. 19, 2399–2424 (2002)
Maloney, A.: To appear
Skenderis K., Taylor M.: The fuzzball proposal for black holes. Phys. Rept. 467, 117–171 (2008)
Crnkovic, C., Witten, E.: Covariant description of canonical formalism in geometrical theories. Print-86-1309 (Princeton)
Crnkovic C.: Symplectic geometry and (super)Poincare algebra in geometrical theories. Nucl. Phys. B 288, 419 (1987)
Lee J., Wald R.M.: Local symmetries and constraints. J. Math. Phys. 31, 725–743 (1990)
van Rees, B.: Dynamics and the gauge/gravity duality. PhD thesis, 2010, to appear
Acknowledgments
We would like to thank Alex Maloney, Jan Smit and Erik Verlinde for discussions. KS acknowledges support from NWO via a VICI grant.
Open Access
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial 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
Communicated by P.T. Chruściel
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Skenderis, K., van Rees, B.C. Holography and Wormholes in 2+1 Dimensions. Commun. Math. Phys. 301, 583–626 (2011). https://doi.org/10.1007/s00220-010-1163-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00220-010-1163-z