- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Complex Liouville String

Scott Collier

Lorenz Eberhardt

Beatrix Mühlmann

Victor A. Rodriguez

PDF

Phys. Rev. Lett. 134, 251602 – Published 25 June, 2025

DOI: https://doi.org/10.1103/k74n-s63l

Abstract

We introduce the complex Liouville string, a solvable string theory defined by coupling two Liouville theories with complex conjugate central charges c∈13+iR on the world sheet. We compute its amplitudes from first principles and establish a duality with a double-scaled two-matrix integral. We also analyze general world sheet boundaries and nonperturbative effects in the genus expansion. By expressing the complex Liouville string as a 2D dilaton gravity theory with a sine potential, we show that it admits both AdS2 and dS2 vacua.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (49)

  1. D. J. Gross and A. A. Migdal, Phys. Rev. Lett. 64, 127 (1990).
  2. M. R. Douglas and S. H. Shenker, Nucl. Phys. B335, 635 (1990).
  3. E. Brezin and V. A. Kazakov, Phys. Lett. B 236, 144 (1990).
  4. N. Seiberg and D. Shih, C.R. Phys. 6, 165 (2005).
  5. S. Collier, L. Eberhardt, B. Mühlmann, and V. A. Rodriguez, SciPost Phys. 16, 057 (2024).
  6. P. Saad, S. H. Shenker, and D. Stanford, arXiv:1903.11115.
  7. S. Collier, L. Eberhardt, B. Mühlmann, and V. A. Rodriguez, arXiv:2409.18759.
  8. S. Collier, L. Eberhardt, B. Mühlmann, and V. A. Rodriguez, SciPost Phys. 18, 154 (2025).
  9. S. Collier, L. Eberhardt, B. Mühlmann, and V. A. Rodriguez, arXiv:2410.09179.
  10. S. Collier, L. Eberhardt, and B. Mühlmann, arXiv:2501.10265.
  11. N. Seiberg, Prog. Theor. Phys. Suppl. 102, 319 (1990).
  12. H. Dorn and H. J. Otto, Nucl. Phys. B429, 375 (1994).
  13. A. B. Zamolodchikov and A. B. Zamolodchikov, Nucl. Phys. B477, 577 (1996).
  14. J. Teschner, Phys. Lett. B 363, 65 (1995).
  15. J. Teschner, Classical Quantum Gravity 18, R153 (2001).
  16. A. Zamolodchikov, Int. J. Mod. Phys. A 19S2, 510 (2004).
  17. A. A. Belavin and A. B. Zamolodchikov, Theor. Math. Phys. 147, 729 (2006).
  18. V. A. Kazakov, Phys. Lett. A 119, 140 (1986).
  19. E. Brezin, M. R. Douglas, V. Kazakov, and S. H. Shenker, Phys. Lett. B 237, 43 (1990).
  20. M. R. Douglas, The two-matrix model, in Random Surfaces and Quantum Gravity (Springer US, Boston, MA, 1991), pp. 77–83.
  21. C. Crnkovic, P. H. Ginsparg, and G. W. Moore, Phys. Lett. B 237, 196 (1990).
  22. B. Eynard and N. Orantin, Commun. Num. Theor. Phys. 1, 347 (2007).
  23. B. Eynard, J. High Energy Phys. 01 (2003) 051.
  24. L. Chekhov, B. Eynard, and N. Orantin, J. High Energy Phys. 12 (2006) 053.
  25. B. Eynard and N. Orantin, arXiv:0705.0958.
  26. M. Mirzakhani, Inventiones Mathematicae 167, 179 (2006).
  27. N. Seiberg and D. Shih, J. High Energy Phys. 02 (2004) 021.
  28. J. Polchinski, Phys. Rev. D 50, R6041 (1994).
  29. B. Balthazar, V. A. Rodriguez, and X. Yin, J. High Energy Phys. 05 (2023) 048.
  30. B. Balthazar, V. A. Rodriguez, and X. Yin, J. High Energy Phys. 05 (2023) 050.
  31. A. B. Zamolodchikov and A. B. Zamolodchikov, arXiv:hep-th/0101152.
  32. J. Cotler and K. Jensen, J. High Energy Phys. 12 (2024) 016.
  33. A. Sen, J. High Energy Phys. 08 (2020) 075.
  34. A. Sen, J. High Energy Phys. 11 (2021) 077.
  35. D. S. Eniceicu, R. Mahajan, C. Murdia, and A. Sen, J. High Energy Phys. 07 (2022) 139.
  36. J. M. Daul, V. A. Kazakov, and I. K. Kostov, Nucl. Phys. B409, 311 (1993).
  37. D. S. Eniceicu, R. Mahajan, C. Murdia, and A. Sen, J. High Energy Phys. 10 (2022) 065.
  38. M. Berkooz, M. Isachenkov, V. Narovlansky, and G. Torrents, J. High Energy Phys. 03 (2019) 079.
  39. V. Narovlansky and H. Verlinde, J. High Energy Phys. 05 (2025) 032.
  40. H. Verlinde and M. Zhang, J. High Energy Phys. 05 (2025) 053.
  41. A. Blommaert, T. G. Mertens, and S. Yao, J. High Energy Phys. 11 (2024) 054.
  42. A. Blommaert, T. G. Mertens, and J. Papalini, J. High Energy Phys. 06 (2025) 050.
  43. T. G. Mertens and G. J. Turiaci, J. High Energy Phys. 01 (2021) 073.
  44. A. Goel, Investigations of holographic duality in two dimensions, Ph.D. thesis, Princeton University, 2022.
  45. D. Anninos and D. M. Hofman, Classical Quantum Gravity 35, 085003 (2018).
  46. D. Anninos and E. Harris, J. High Energy Phys. 11 (2022) 166.
  47. S. Collier, L. Eberhardt, and B. Mühlmann, SciPost Phys. 18, 131 (2025).
  48. G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15, 2752 (1977).
  49. G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15, 2738 (1977).

Outline

Information

Phys. Rev. Lett. 134, 251602– Published 25 June, 2025
  • Received 15 February 2025
  • Accepted 9 June 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation