- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

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

Holographic timelike c-function

Dimitrios Giataganas

PDF

Phys. Rev. D 114, 026027 – Published 22 July, 2026

DOI: https://doi.org/10.1103/h7x9-39zs

Abstract

The integration of high-energy degrees of freedom along the renormalization group (RG) flow in Poincaré-invariant theories is captured by a monotonic c-function. For such theories, holographic c-functions have been constructed using entanglement entropy. However, in theories with broken Lorentz invariance, these constructions generally fail, reflecting both the violation of entanglement RG monotonicity and its limitations in capturing essential features of nonrelativistic RG flows. Since many quantum many-body systems lack Lorentz invariance, it is important to identify a quantity that captures the decrease of effective degrees of freedom along such flows. We show that the recently introduced holographic timelike entanglement entropy naturally gives rise to a new c-function applicable to all such theories, which moreover obeys a geometric upper bound on its rate of change. We further demonstrate the existence of this c-function in theories with Lifshitz and hyperscaling-violating fixed points, showing that, provided the null energy condition and thermodynamic stability are satisfied, it obeys the expected RG monotonicity.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (34)

  1. A. B. Zamolodchikov, Irreversibility of the flux of the renormalization group in a 2D field theory, JETP Lett. 43, 730 (1986).
  2. John L. Cardy, Is there a c theorem in four-dimensions?, Phys. Lett. B 215, 749 (1988).
  3. Zohar Komargodski and Adam Schwimmer, On renormalization group flows in four dimensions, J. High Energy Phys. 12 (2011) 099.
  4. D. Z. Freedman, S. S. Gubser, K. Pilch, and N. P. Warner, Renormalization group flows from holography supersymmetry and a c theorem, Adv. Theor. Math. Phys. 3, 363 (1999).
  5. Shinsei Ryu and Tadashi Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96, 181602 (2006).
  6. Shinsei Ryu and Tadashi Takayanagi, Aspects of holographic entanglement entropy, J. High Energy Phys. 08 (2006) 045.
  7. Robert C. Myers and Aninda Sinha, Seeing a c-theorem with holography, Phys. Rev. D 82, 046006 (2010).
  8. Robert C. Myers and Aninda Sinha, Holographic c-theorems in arbitrary dimensions, J. High Energy Phys. 01 (2011) 125.
  9. Horacio Casini, Marina Huerta, and Robert C. Myers, Towards a derivation of holographic entanglement entropy, J. High Energy Phys. 05 (2011) 036.
  10. Ling-Yan Hung, Robert C. Myers, and Michael Smolkin, Some calculable contributions to holographic entanglement entropy, J. High Energy Phys. 08 (2011) 039.
  11. Hong Liu and Mark Mezei, A Refinement of entanglement entropy and the number of degrees of freedom, J. High Energy Phys. 04 (2013) 162.
  12. Chong-Sun Chu and Dimitrios Giataganas, c-Theorem for anisotropic RG flows from holographic entanglement entropy, Phys. Rev. D 101, 046007 (2020).
  13. Kenneth G. Wilson, The renormalization group: Critical phenomena and the Kondo problem, Rev. Mod. Phys. 47, 773 (1975).
  14. Sera Cremonini and Xi Dong, Constraints on renormalization group flows from holographic entanglement entropy, Phys. Rev. D 89, 065041 (2014).
  15. Brian Swingle, Entanglement does not generally decrease under renormalization, J. Stat. Mech. (2014) P10041.
  16. Kazuki Doi, Jonathan Harper, Ali Mollabashi, Tadashi Takayanagi, and Yusuke Taki, Timelike entanglement entropy, J. High Energy Phys. 05 (2023) 052.

  17. Timelike entanglement entropy and pseudoentropies have been shown to contain valuable information about quantum field theories and their phase transitions, and are the subject of active recent research [18, 19, 20, 21, 22, 23, 24, 25, 26].

  18. Mir Afrasiar, Jaydeep Kumar Basak, and Dimitrios Giataganas, Timelike entanglement entropy and phase transitions in non-conformal theories, J. High Energy Phys. 07 (2024) 243.
  19. Mir Afrasiar, Jaydeep Kumar Basak, and Dimitrios Giataganas, Holographic timelike entanglement entropy in non-relativistic theories, J. High Energy Phys. 05 (2025) 205.
  20. Hiroki Kanda, Taishi Kawamoto, Yu-ki Suzuki, Tadashi Takayanagi, Kenya Tasuki, and Zixia Wei, Entanglement phase transition in holographic pseudo entropy, J. High Energy Phys. 03 (2024) 060.
  21. Chong-Sun Chu and Himanshu Parihar, Time-like entanglement entropy in AdS/BCFT, J. High Energy Phys. 06 (2023) 173.
  22. Pawel Caputa, Bowen Chen, Tadashi Takayanagi, and Takashi Tsuda, Thermal pseudo-entropy, J. High Energy Phys. 01 (2025) 003.
  23. K. Narayan, de Sitter space, extremal surfaces, and time entanglement, Phys. Rev. D 107, 126004 (2023).
  24. Jaydeep Kumar Basak, Adrita Chakraborty, Chong-Sun Chu, Dimitrios Giataganas, and Himanshu Parihar, Massless Lifshitz field theory for arbitrary z, J. High Energy Phys. 05 (2024) 284.
  25. Dibakar Roychowdhury, Field theory aspects of η-deformed superstring background, J. High Energy Phys. 06 (2025) 161.
  26. Chong-Sun Chu and Himanshu Parihar, Timelike entanglement entropy with gravitational anomalies, J. High Energy Phys. 08 (2025) 038.
  27. H. Casini and M. Huerta, A c-theorem for the entanglement entropy, J. Phys. A 40, 7031 (2007).
  28. Robert C. Myers and Ajay Singh, Comments on Holographic Entanglement Entropy and RG Flows, J. High Energy Phys. 04 (2012) 122.
  29. Robert M. Wald, General Relativity (Chicago Univ. Pr., Chicago, USA, 1984).
  30. Roman V. Buniy, Stephen D. H. Hsu, and Brian M. Murray, The Null energy condition and instability, Phys. Rev. D 74, 063518 (2006).
  31. S. Dubovsky, T. Gregoire, A. Nicolis, and R. Rattazzi, Null energy condition and superluminal propagation, J. High Energy Phys. 03 (2006) 025.
  32. Carlos Hoyos and Peter Koroteev, On the Null energy condition and causality in Lifshitz holography, Phys. Rev. D 82, 084002 (2010); 82, 109905(E) (2010).
  33. L. Girardello, M. Petrini, M. Porrati, and A. Zaffaroni, Novel local CFT and exact results on perturbations of N=4 superYang Mills from AdS dynamics, J. High Energy Phys. 12 (1998) 022.
  34. Dimitrios Giataganas, Timelike entanglement entropy and renormalization group flow irreversibility, arXiv:2512.16499.

Outline

Information

Phys. Rev. D 114, 026027– Published 22 July, 2026
  • Received 4 June 2025
  • Accepted 2 June 2026
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