Abstract
Tensionless string theory on AdS3 × S3 × \( \mathcal{M} \) is explored in the limit that the strings wind the asymptotic boundary a large number of times. Although the worldsheet is usually thought to be localised to the AdS boundary, we argue that the string can actually probe the bulk geometry in this limit. In particular, we show that correlation functions can be expressed in terms of a minimal-area worldsheet propagating in AdS3. We then relate the classical motion of the string to the twistor-like free field description of the tensionless worldsheet theory. Finally, we consider a particular dimensional reduction of AdS3 to AdS2, and show that the effective action of the worldsheet formally resembles the one-dimensional Schwarzian theory of JT gravity with conical defects.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M.R. Gaberdiel and R. Gopakumar, Tensionless string spectra on AdS3, JHEP 05 (2018) 085 [arXiv:1803.04423] [INSPIRE].
L. Eberhardt, M.R. Gaberdiel and R. Gopakumar, The Worldsheet Dual of the Symmetric Product CFT, JHEP 04 (2019) 103 [arXiv:1812.01007] [INSPIRE].
L. Eberhardt, M.R. Gaberdiel and R. Gopakumar, Deriving the AdS3/CFT2 correspondence, JHEP 02 (2020) 136 [arXiv:1911.00378] [INSPIRE].
A. Dei, M.R. Gaberdiel, R. Gopakumar and B. Knighton, Free field world-sheet correlators for AdS3, JHEP 02 (2021) 081 [arXiv:2009.11306] [INSPIRE].
L. Eberhardt, AdS3/CFT2 at higher genus, JHEP 05 (2020) 150 [arXiv:2002.11729] [INSPIRE].
B. Knighton, Higher genus correlators for tensionless AdS3 strings, JHEP 04 (2021) 211 [arXiv:2012.01445] [INSPIRE].
H. Bertle, A. Dei and M.R. Gaberdiel, Stress-energy tensor correlators from the world-sheet, JHEP 03 (2021) 036 [arXiv:2012.08486] [INSPIRE].
M.R. Gaberdiel and K. Naderi, The physical states of the Hybrid Formalism, JHEP 10 (2021) 168 [arXiv:2106.06476] [INSPIRE].
L. Eberhardt, Partition functions of the tensionless string, JHEP 03 (2021) 176 [arXiv:2008.07533] [INSPIRE].
J.M. Maldacena and H. Ooguri, Strings in AdS3 and SL(2, R) WZW model. I: The Spectrum, J. Math. Phys. 42 (2001) 2929 [hep-th/0001053] [INSPIRE].
L. Eberhardt, Summing over Geometries in String Theory, JHEP 05 (2021) 233 [arXiv:2102.12355] [INSPIRE].
O. Lunin and S.D. Mathur, Correlation Functions for MN/SN Orbifolds, Commun. Math. Phys. 219 (2001) 399 [hep-th/0006196] [INSPIRE].
A. Dei and L. Eberhardt, Correlators of the symmetric product orbifold, JHEP 01 (2020) 108 [arXiv:1911.08485] [INSPIRE].
M.R. Gaberdiel, R. Gopakumar, B. Knighton and P. Maity, From symmetric product CFTs to AdS3, JHEP 05 (2021) 073 [arXiv:2011.10038] [INSPIRE].
R. Gopakumar, From free fields to AdS, Phys. Rev. D 70 (2004) 025009 [hep-th/0308184] [INSPIRE].
R. Gopakumar, From free fields to AdS. II, Phys. Rev. D 70 (2004) 025010 [hep-th/0402063] [INSPIRE].
R. Gopakumar, From free fields to AdS: III, Phys. Rev. D 72 (2005) 066008 [hep-th/0504229] [INSPIRE].
S. Hamidi and C. Vafa, Interactions on Orbifolds, Nucl. Phys. B 279 (1987) 465 [INSPIRE].
K. Roumpedakis, Comments on the SN orbifold CFT in the large N-limit, JHEP 07 (2018) 038 [arXiv:1804.03207] [INSPIRE].
P. Maity, Scattering and Strebel graphs, SciPost Phys. 13 (2022) 010 [arXiv:2108.09458] [INSPIRE].
P. Bantay, Permutation orbifolds, Nucl. Phys. B 633 (2002) 365 [hep-th/9910079] [INSPIRE].
G.H. Hardy and E.M. Wright, Introduction to the Theory of Numbers, sixth edition, Oxford University Press (1938) [https://doi.org/10.1080/00107510903184414].
J.-L. Nicolas and G. Robin, Highly Composite Numbers by Srinivasa Ramanujan, Ramanujan J. 1 (1997) 119.
M. Young, Mathoverflow answer, https://mathoverflow.net/questions/115100/numerical-evaluation-of-the-petersson-product-of-elliptic-modular-forms.
I.Y. Arefeva and A.A. Bagrov, Holographic dual of a conical defect, Teor. Mat. Fiz. 182 (2014) 3 [INSPIRE].
D. Berenstein, D. Grabovsky and Z. Li, Aspects of holography in conical AdS3, JHEP 04 (2023) 029 [arXiv:2205.02256] [INSPIRE].
N. Benjamin, S. Collier and A. Maloney, Pure Gravity and Conical Defects, JHEP 09 (2020) 034 [arXiv:2004.14428] [INSPIRE].
B. Zwiebach, How covariant closed string theory solves a minimal area problem, Commun. Math. Phys. 136 (1991) 83 [INSPIRE].
N. Moeller, Closed bosonic string field theory at quartic order, JHEP 11 (2004) 018 [hep-th/0408067] [INSPIRE].
N. Berkovits, C. Vafa and E. Witten, Conformal field theory of AdS background with Ramond-Ramond flux, JHEP 03 (1999) 018 [hep-th/9902098] [INSPIRE].
F. Bhat, R. Gopakumar, P. Maity and B. Radhakrishnan, Twistor coverings and Feynman diagrams, JHEP 05 (2022) 150 [arXiv:2112.05115] [INSPIRE].
B. Eynard, Lectures notes on compact Riemann surfaces, arXiv:1805.06405.
M.R. Gaberdiel and R. Gopakumar, String Dual to Free N = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 127 (2021) 131601 [arXiv:2104.08263] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, The worldsheet dual of free super Yang-Mills in 4D, JHEP 11 (2021) 129 [arXiv:2105.10496] [INSPIRE].
M.R. Gaberdiel and F. Galvagno, Worldsheet dual of free \( \mathcal{N} \) = 2 quiver gauge theories, JHEP 10 (2022) 077 [arXiv:2206.08795] [INSPIRE].
R. Jackiw, Lower Dimensional Gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
M.R. Gaberdiel, B. Knighton and J. Vošmera, D-branes in AdS3 × S3 × 𝕋4 at k = 1 and their holographic duals, JHEP 12 (2021) 149 [arXiv:2110.05509] [INSPIRE].
C. Bachas and M. Petropoulos, Anti-de Sitter D-branes, JHEP 02 (2001) 025 [hep-th/0012234] [INSPIRE].
A. Banerjee, A. Kundu and R.R. Poojary, Strings, branes, Schwarzian action and maximal chaos, Phys. Lett. B 838 (2023) 137632 [arXiv:1809.02090] [INSPIRE].
A. Banerjee, A. Kundu and R. Poojary, Maximal Chaos from Strings, Branes and Schwarzian Action, JHEP 06 (2019) 076 [arXiv:1811.04977] [INSPIRE].
L.V. Iliesiu, S.S. Pufu, H. Verlinde and Y. Wang, An exact quantization of Jackiw-Teitelboim gravity, JHEP 11 (2019) 091 [arXiv:1905.02726] [INSPIRE].
T.G. Mertens and G.J. Turiaci, Solvable Models of Quantum Black Holes: A Review on Jackiw-Teitelboim Gravity, arXiv:2210.10846 [INSPIRE].
J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys. 104 (1986) 207 [INSPIRE].
E. Mefford and K. Suzuki, Jackiw-Teitelboim quantum gravity with defects and the Aharonov-Bohm effect, JHEP 05 (2021) 026 [arXiv:2011.04695] [INSPIRE].
J. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS2 backreaction and holography, JHEP 07 (2016) 139 [arXiv:1606.03438] [INSPIRE].
H. Geng et al., Jackiw-Teitelboim Gravity from the Karch-Randall Braneworld, Phys. Rev. Lett. 129 (2022) 231601 [arXiv:2206.04695] [INSPIRE].
H. Geng, Aspects of AdS2 quantum gravity and the Karch-Randall braneworld, JHEP 09 (2022) 024 [arXiv:2206.11277] [INSPIRE].
F. Deng, Y.-S. An and Y. Zhou, JT gravity from partial reduction and defect extremal surface, JHEP 02 (2023) 219 [arXiv:2206.09609] [INSPIRE].
A. Ghosh, H. Maxfield and G.J. Turiaci, A universal Schwarzian sector in two-dimensional conformal field theories, JHEP 05 (2020) 104 [arXiv:1912.07654] [INSPIRE].
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
M.R. Gaberdiel, R. Gopakumar, B. Knighton and P. Maity, Work in progress.
F. Aprile and P. Vieira, Large p explorations. From SUGRA to big STRINGS in Mellin space, JHEP 12 (2020) 206 [arXiv:2007.09176] [INSPIRE].
L. Eberhardt, A perturbative CFT dual for pure NS–NS AdS3 strings, J. Phys. A 55 (2022) 064001 [arXiv:2110.07535] [INSPIRE].
T. Ekedahl, S. Lando, M. Shapiro and A. Vainshtein, On Hurwitz numbers and Hodge integrals, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 328 (1999) 1175.
A. Maloney and E. Witten, Averaging over Narain moduli space, JHEP 10 (2020) 187 [arXiv:2006.04855] [INSPIRE].
N. Benjamin, C.A. Keller, H. Ooguri and I.G. Zadeh, Narain to Narnia, Commun. Math. Phys. 390 (2022) 425 [arXiv:2103.15826] [INSPIRE].
A. Maloney, H. Maxfield and G.S. Ng, A conformal block Farey tail, JHEP 06 (2017) 117 [arXiv:1609.02165] [INSPIRE].
J. Kames-King, A. Kanargias, B. Knighton and M. Usatyuk, The Lion, the Witch, and the Wormhole: Ensemble averaging the symmetric product orbifold, work in progress.
P. Saad, S.H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE].
D. Gaiotto and M. Rapčák, Vertex Algebras at the Corner, JHEP 01 (2019) 160 [arXiv:1703.00982] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2207.01293
Rights and permissions
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.
About this article
Cite this article
Knighton, B. Classical geometry from the tensionless string. J. High Energ. Phys. 2023, 5 (2023). https://doi.org/10.1007/JHEP05(2023)005
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2023)005