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On Casimir Energy and Mutual Information in Non-relativistic Backgrounds

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Abstract

We apply the AdS/CFT correspondence in considering the Casimir energy and some non-local entanglement measures in the non-relativistic backgrounds for general dynamical exponent z with and without hyperscaling violation exponent 𝜃. In such background, we use holographic methods and compute the mutual information and tripartite information. We also consider the monogamy of holographic mutual information in the Schrödinger-type geometry and by numerical analysis we show that this quantity is monogamous.

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References

  1. Bordag, M., Klimchitskaya, G.L., Mohideen, U., Mostepanenko, V.M.: Advances in the Casimir Effect. University Press, Oxfords (2009)

    Book  Google Scholar 

  2. Milton, K.A.: The Casimir effect: recent controversies and progress. J. Phys. A 37, R209 (2004). https://doi.org/10.1088/0305-4470/37/38/R01[hep-th/0406024]

    Article  ADS  MathSciNet  Google Scholar 

  3. Milton, K.A.: The Casimir effect: physical manifestations of zero point energy. arXiv:9901011 [hep-th]

  4. Milton, K.A., Parashar, P., Brevik, I., Kennedy, G.: Self-stress on a dielectric ball and Casimir-polder forces. Annals Phys. 412, 168008 (2020). https://doi.org/10.1016/j.aop.2019.168008. arXiv:1909.05721 [hep-th]

    Article  MathSciNet  Google Scholar 

  5. Brevik, I., Parashar, P., Shajesh, K.V.: Casimir force for magnetodielectric media. Phys. Rev. A 98(3), 032509 (2018). https://doi.org/10.1103/PhysRevA.98.032509. arXiv:1808.02205[physics.class-ph]

    Article  ADS  Google Scholar 

  6. Lambrecht, A.: The Casimir effect: a force from nothing. Physics World, pp. 28–32, ISSN: 0953-8585. http://casimir-network.fr/IMG/pdf/Casimir_20effect.pdf (2002)

  7. Trang, T.N.: Casimir effect and vacuum fluctuations. http://www.hep.caltech.edu/phys199/lectures/lect5_6_cas.pdf (2003)

  8. Pejhan, H., Tanhayi, M.R., Takook, M.V.: Casimir effect for a scalar field via Krein quantization. Annals Phys. 341, 195–204 (2014). arXiv:1204.6001[math-ph]

    Article  ADS  MathSciNet  Google Scholar 

  9. Hasani, M., Tavakoli, F., Tanhayi, M.R.: Radial Casimir effect in a sphere through the Krein space quantization. Mod. Phys. Lett. A 27, 1250096 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  10. Ghaffari, A, Karimaghaee, S, Tanhayi, M.R.: Vacuum energy in two dimensional box through the Krein quantization. Int. J .Theor. Phys. 56, 887–897 (2017)

    Article  Google Scholar 

  11. Maldacena, J.M.: The large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2, 231 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  12. Maldacena, J.M.: . Int. J. Theor. Phys. 38, 1113 (1999). arXiv:9711200 [hep-th]

    Article  Google Scholar 

  13. Gubser, S.S., Klebanov, I.R., Polyakov, A.M.: Gauge theory correlators from non-critical string theory. Phys. Lett. B 428, 105 (1998). arXiv:9802109 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  14. Witten, E.: Anti-de Sitter space and holography. Adv. Theor. Math. Phys. 2, 253 (1998). arXiv:9802150 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  15. Aharony, O., Gubser, S.S., Maldacena, J.M., Ooguri, H., Oz, Y.: Large N field theories, string theory and gravity. Phys. Rept. 323, 183 (2000). arXiv:9905111 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  16. Horowitz, G.T., Myers, R.C.: . Phys. Rev. D59, 026005 (1999). arXiv:9808079 [hep-th]

    ADS  Google Scholar 

  17. Son, D.T.: Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry. Phys. Rev. D 78, 046003 (2008). arXiv:0804.3972 [hep-th]

    Article  ADS  Google Scholar 

  18. Balasubramanian, K., McGreevy, J.: Gravity duals for non-relativistic CFTs. Phys. Rev. Lett. 101, 061601 (2008). arXiv:0804.4053 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  19. Goldberger, W.D.: AdS/CFT duality for non-relativistic field theory. JHEP 0903, 069 (2009). arXiv:0806.2867 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  20. Barbon, J.L.F., Fuertes, C.A.: On the spectrum of nonrelativistic AdS/CFT. JHEP 0809, 030 (2008). arXiv:0806.3244 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  21. Kachru, S., Liu, X., Mulligan, M.: Gravity duals of lifshitz-like fixed points. Phys. Rev. D 78, 106005 (2008). arXiv:0808.1725 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  22. Taylor, M.: Non-relativistic holography, arXiv:0812.0530 [hep-th]

  23. Ryu, S., Takayanagi, T.: Aspects of holographic entanglement entropy. JHEP 0608, 045 (2006). https://doi.org/10.1088/1126-6708/2006/08/045[hep-th/0605073]

    Article  ADS  MathSciNet  Google Scholar 

  24. Hayden, P., Headrick, M., Maloney, A.: Holographic mutual information is monogamous. Phys. Rev. D 87(4), 046003 (2013). https://doi.org/10.1103/PhysRevD.87.046003. arXiv:1107.2940 [hep-th]

    Article  ADS  Google Scholar 

  25. Dong, X., Harrison, S., Kachru, S., Torroba, G., Wang, H.: Aspects of holography for theories with hyperscaling violation. arXiv:1201.1905 [hep-th]

  26. Alishahiha, M., Colgain, E.O., Yavartanoo, H.: Charged black branes with hyperscaling violating factor. JHEP 1211, 137 (2012). https://doi.org/10.1007/JHEP11(2012)137. arXiv:1209.3946 [hep-th]

    Article  ADS  Google Scholar 

  27. Alishahiha, M., Astaneh, A.F., Mozaffar, M.R.M., Mollabashi, A.: Complexity growth with lifshitz scaling and hyperscaling violation. JHEP 1807, 042 (2018). https://doi.org/10.1007/JHEP07(2018)042. arXiv:1802.06740 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  28. Taylor, M.: Lifshitz holography. Class. Quant. Grav. 33(3), 033001 (2016). https://doi.org/10.1088/0264-9381/33/3/033001. arXiv:1512.03554 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  29. Kim, B.S.: Schrödinger holography with and without hyperscaling violation. JHEP 1206, 116 (2012). https://doi.org/10.1007/JHEP06(2012)116. arXiv:1202.6062 [hep-th]

    Article  ADS  Google Scholar 

  30. Casini, H., Huerta, M.: Remarks on the entanglement entropy for disconnected regions. JHEP 0903, 048 (2009). arXiv:0812.1773 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  31. Wolf, M.M., Verstraete, F., Hastings, M.B., Cirac, J.I.: Area laws in quantum systems: mutual information and correlations. Phys. Rev. Lett. 100 (7), 070502 (2008). https://doi.org/10.1103/PhysRevLett.100.070502. arXiv:0704.3906[quant-ph]

    Article  ADS  MathSciNet  Google Scholar 

  32. Headrick, M.: Entanglement Renyi entropies in holographic theories. Phys. Rev. D 82, 126010 (2010). arXiv:1006.0047 [hep-th]

    Article  ADS  Google Scholar 

  33. Fischler, W., Kundu, A., Kundu, S.: Holographic mutual information at finite temperature. Phys. Rev. D 87, 126012 (2013). arXiv:1212.4764 [hep-th]

    Article  ADS  Google Scholar 

  34. Mirabi, S., Tanhayi, M.R., Vazirian, R.: On the monogamy of holographic n-partite information. Phys. Rev. D 93(10), 104049 (2016). https://doi.org/10.1103/PhysRevD.93.104049. arXiv:1603.00184 [hep-th]

    Article  ADS  Google Scholar 

  35. Headrick, M., Takayanagi, T.: A holographic proof of the strong subadditivity of entanglement entropy. Phys. Rev. D 76, 106013 (2007). https://doi.org/10.1103/PhysRevD.76.106013. arXiv:0704.3719 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  36. Allais, A., Tonni, E.: Holographic evolution of the mutual information. JHEP 1201, 102 (2012). 10.1007/JHEP01(2012)102. arXiv:1110.1607 [hep-th]

    Article  ADS  Google Scholar 

  37. Wall, A.C.: Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy. Class. Quant. Grav. 31(22), 225007 (2014). https://doi.org/10.1088/0264-9381/31/22/225007. arXiv:1211.3494 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  38. Alishahiha, M., Mozaffar, M.R.M., Tanhayi, M.R.: On the time evolution of holographic n-partite information. JHEP 1509, 165 (2015). https://doi.org/10.1007/JHEP09(2015)165. arXiv:1406.7677 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  39. Flory, M., Erdmenger, J., Fernandez, D., Megias, E., Straub, E., Witkowski, P.: Time dependence of entanglement for steady state formation in AdS3/CFT2. J. Phys. Conf. Ser. 942(1), 012010 (2017). https://doi.org/10.1088/1742-6596/942/1/012010. arXiv:1709.08614 [hep-th]

    Article  Google Scholar 

  40. Tanhayi, M.R., Vazirian, R.: Higher-curvature corrections to holographic entanglement with momentum dissipation. Eur. Phys. J. C 78(2), 162 (2018). https://doi.org/10.1140/epjc/s10052-018-5620-8. arXiv:1610.08080 [hep-th]

    Article  ADS  Google Scholar 

  41. Aref’eva, I., Volovich, I.: Holographic photosynthesis. arXiv:1603.09107 [hep-th]

  42. Tanhayi, M.R.: Universal terms of holographic entanglement entropy in theories with hyperscaling violation. Phys. Rev. D 97(10), 106008 (2018). https://doi.org/10.1103/PhysRevD.97.106008. arXiv:1711.10526 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  43. Erdmenger, J., Fernandez, D., Flory, M., Megias, E., Straub, A.K., Witkowski, P.: Time evolution of entanglement for holographic steady state formation. JHEP 1710, 034 (2017). https://doi.org/10.1007/JHEP10(2017)034. arXiv:1705.04696 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgments

We would like to thank Mohsen Alishahiha, Amin Akhavan and Reza Pirmoradian for his useful comments and related discussions.

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  1. Department of Physics, Faculty of Basic Science, Islamic Azad University Central Tehran Branch (IAUCTB), Tehran, P.O. Box 14676-86831, Iran

    M. Belyad & M. Reza Tanhayi

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Correspondence to M. Reza Tanhayi.

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Belyad, M., Tanhayi, M.R. On Casimir Energy and Mutual Information in Non-relativistic Backgrounds. Int J Theor Phys 59, 1905–1916 (2020). https://doi.org/10.1007/s10773-020-04462-9

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