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Higher-curvature corrections to holographic mutual information

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Abstract

In this paper, we study some non-local measurements of quantum correlations in extended gravities with higher-order curvature terms, including conformal gravity. Precisely, we consider higher-curvature correction on holographic mutual information in conformal gravity. There is in fact one deformation in the states because of the higher-curvature corrections. Here by making use of the holographic methods, we study the deformation in the holographic mutual information due to the higher-curvature terms. We also address the change in the quantum phase transition due to these deformations.

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References

  1. 1.

    Stelle, K.S.: Renormalization of higher derivative quantum gravity. Phys. Rev. D 16, 953 (1977)

  2. 2.

    Tanhayi, M.R., Dengiz, S., Tekin, B.: Unitarity of Weyl-invariant new massive gravity and generation of graviton mass via symmetry breaking. Phys. Rev. D 85, 064008 (2012). https://doi.org/10.1103/PhysRevD.85.064008. arXiv:1112.2338 [hep-th]

  3. 3.

    Tanhayi, M.R., Dengiz, S., Tekin, B.: Weyl-invariant higher curvature gravity theories in \(n\) dimensions. Phys. Rev. D 85, 064016 (2012). https://doi.org/10.1103/PhysRevD.85.064016. arXiv:1201.5068 [hep-th]

  4. 4.

    Tanhayi, M.R., Pejhan, H., Takook, M.V.: Conformal linear gravity in de Sitter space II. Eur. Phys. J. C 72, 2052 (2012). https://doi.org/10.1140/epjc/s10052-012-2052-8. arXiv:1105.3060 [gr-qc]

  5. 5.

    Rouhani, S., Takook, M.V., Tanhayi, M.R.: Linear Weyl gravity in de Sitter universe. JHEP 1012, 044 (2010). https://doi.org/10.1007/JHEP12(2010)044. arXiv:0903.2670 [gr-qc]

  6. 6.

    Dehghani, M., Rouhani, S., Takook, M.V., Tanhayi, M.R.: Conformally invariant ’massless’ spin-2 field in the de Sitter universe. Phys. Rev. D 77, 064028 (2008). https://doi.org/10.1103/PhysRevD.77.064028. arXiv:0805.2227 [gr-qc]

  7. 7.

    Behroozi, S., Rouhani, S., Takook, M.V., Tanhayi, M.R.: Conformally invariant wave equations and massless fields in de Sitter spacetime. Phys. Rev. D 74, 124014 (2006). https://doi.org/10.1103/PhysRevD.74.124014. arXiv:gr-qc/0512105

  8. 8.

    Maldacena, J.: Einstein gravity from conformal gravity. arXiv:1105.5632 [hep-th]

  9. 9.

    Anderson, M.T.: \(L^2\) curvature and volume renormalization of AHE metrics on 4-manifolds. Math. Res. Lett. 8, 171 (2001). arXiv:math/001105

  10. 10.

    Alishahiha, M., Astaneh, A.F., Mozaffar, M.R.: Mohammadi: holographic entanglement entropy for 4D conformal gravity. JHEP 1402, 008 (2014). https://doi.org/10.1007/JHEP02(2014)008. arXiv:1311.4329 [hep-th]

  11. 11.

    Hartnoll, S.A.: Horizons, holography and condensed matter. arXiv:1106.4324 [hep-th]

  12. 12.

    Hartnoll, S.A.: Lectures on holographic methods for condensed matter physics. Class. Quantum Gravity 26, 224002 (2009). https://doi.org/10.1088/0264-9381/26/22/224002. arXiv:0903.3246 [hep-th]

  13. 13.

    Hartnoll, S.A., Polchinski, J., Silverstein, E., Tong, D.: Towards strange metallic holography. JHEP 1004, 120 (2010). https://doi.org/10.1007/JHEP04(2010)120. arXiv:0912.1061 [hep-th]

  14. 14.

    Faulkner, T., Iqbal, N., Liu, H., McGreevy, J., Vegh, D.: From black holes to strange metals. arXiv:1003.1728 [hep-th]

  15. 15.

    Lu, H., Pang, Y., Pope, C.N., Vazquez-Poritz, J.F.: AdS and Lifshitz black holes in conformal and Einstein–Weyl gravities. Phys. Rev. D 86, 044011 (2012). arXiv:1204.1062 [hep-th]

  16. 16.

    Nishioka, T., Ryu, S., Takayanagi, T.: Holographic entanglement entropy: an overview. J. Phys. A 42, 504008 (2009). https://doi.org/10.1088/1751-8113/42/50/504008. arXiv:0905.0932 [hep-th]

  17. 17.

    Hubeny, V.E., Rangamani, M., Takayanagi, T.: A covariant holographic entanglement entropy proposal. JHEP 0707, 062 (2007). https://doi.org/10.1088/1126-6708/2007/07/062. arXiv:0705.0016 [hep-th]

  18. 18.

    Hung, L.Y., Myers, R.C., Smolkin, M.: On holographic entanglement entropy and higher curvature gravity. JHEP 1104, 025 (2011). https://doi.org/10.1007/JHEP04(2011)025. arXiv:1101.5813 [hep-th]

  19. 19.

    Fursaev, D.V., Patrushev, A., Solodukhin, S.N.: Distributional geometry of squashed cones. Phys. Rev. D 88(4), 044054 (2013). https://doi.org/10.1103/PhysRevD.88.044054. arXiv:1306.4000 [hep-th]

  20. 20.

    Dong, X.: Holographic entanglement entropy for general higher derivative gravity. JHEP 1401, 044 (2014). https://doi.org/10.1007/JHEP01(2014)044. arXiv:1310.5713 [hep-th]

  21. 21.

    Camps, J.: Generalized entropy and higher derivative gravity. JHEP 1403, 070 (2014). https://doi.org/10.1007/JHEP03(2014)070. arXiv:1310.6659 [hep-th]

  22. 22.

    de Boer, J., Kulaxizi, M., Parnachev, A.: Holographic entanglement entropy in lovelock gravities. JHEP 1107, 109 (2011). https://doi.org/10.1007/JHEP07(2011)109. arXiv:1101.5781 [hep-th]

  23. 23.

    Mozaffar, M.R.M., Mollabashi, A., Sheikh-Jabbari, M.M., Vahidinia, M.H.: Holographic entanglement entropy, field redefinition invariance and higher derivative gravity theories. Phys. Rev. D, 94(4), 046002 (2016). https://doi.org/10.1103/PhysRevD.94.046002. arXiv:1603.05713 [hep-th]

  24. 24.

    Bueno, P., Ramirez, P.F.: Higher-curvature corrections to holographic entanglement entropy in geometries with hyperscaling violation. JHEP 1412, 078 (2014). https://doi.org/10.1007/JHEP12(2014)078. arXiv:1408.6380 [hep-th]

  25. 25.

    Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009). https://doi.org/10.1103/RevModPhys.81.865. arXiv:quant-ph/0702225

  26. 26.

    Bernamonti, A., Copland, N., Craps, B., Galli, F.: Holographic thermalization of mutual and tripartite information in 2d CFTs. PoS Corfu 2012, 120 (2013). arXiv:1212.0848 [hep-th]

  27. 27.

    Casini, H., Huerta, M.: Remarks on the entanglement entropy for disconnected regions. JHEP 0903, 048 (2009). https://doi.org/10.1088/1126-6708/2009/03/048. arXiv:0812.1773 [hep-th]

  28. 28.

    Headrick, M.: Entanglement Renyi entropies in holographic theories. Phys. Rev. D 82, 126010 (2010). https://doi.org/10.1103/PhysRevD.82.126010. arXiv:1006.0047 [hep-th]

  29. 29.

    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]

  30. 30.

    Mozaffar, M.R.M., Mollabashi, A., Omidi, F.: Holographic mutual information for singular surfaces. JHEP 1512, 082 (2015). https://doi.org/10.1007/JHEP12(2015)082. arXiv:1511.00244 [hep-th]

  31. 31.

    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]

  32. 32.

    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]

  33. 33.

    Pastawski, F., Yoshida, B., Harlow, D., Preskill, J.: Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence. JHEP 1506, 149 (2015). https://doi.org/10.1007/JHEP06(2015)149. arXiv:1503.06237 [hep-th]

  34. 34.

    Almheiri, A., Dong, X., Harlow, D.: Bulk locality and quantum error correction in AdS/CFT. J. High Energy Phys. 2015(4), 163 (2015)

  35. 35.

    Headrick, M., Takayanagi, T.: A holographic proof of the strong subadditivity of entanglement entropy. Phys. Rev. D 76, 106013 (2007). arXiv:0704.3719

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Acknowledgements

The author would like to thank Mohsen Alishahiha, for his helpful comments and discussions. MRT also wishes to acknowledge A. Akhvan and F. Omidi for some their comments. This work has been supported in parts by IAUCTB.

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Correspondence to M. Reza Tanhayi.

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Appendix: some useful mathematical relations

Appendix: some useful mathematical relations

Here in this appendix, we present some useful relations that we have used in this paper. Let us choose a five-dimensional metric with coordinate trxyz as follows

$$\begin{aligned} \left( \begin{array}{ccccc} -\frac{f(r)}{r^2} & 0 & 0 & 0 & 0 \\ 0 & \frac{1}{r^2 f(r)} & 0 & 0 & 0 \\ 0 & 0 & \frac{1}{r^2} & 0 & 0 \\ 0 & 0 & 0 & \frac{1}{r^2} & 0 \\ 0 & 0 & 0 & 0 & \frac{1}{r^2} \\ \end{array} \right) \end{aligned}$$

The determinant of the induced metric reads as

$$\begin{aligned} \frac{1}{r^6 f(r)}+\frac{x'(r)^2}{r^6} \end{aligned}$$

Therefore, two normal vectors are obtained as

$$\begin{aligned}&\left\{ \frac{1}{\sqrt{\frac{r^2}{f(r)}}},0,0,0,0\right\} ,\\&\quad \left\{ 0,-\frac{x'(r)}{\sqrt{r^2 f(r) x'(r)^2+r^2}},\frac{1}{\sqrt{r^2 f(r) x'(r)^2+r^2}},0,0\right\} \end{aligned}$$

The nonzero component of the extrinsic curvature ten reads as

$$\begin{aligned} {{{\mathcal {K}}}}_{11} &= \frac{-r f'(r) x'(r)+2 f(r)^2 x'(r)^3+2 f(r) \left( x'(r)-r x''(r)\right) }{2 r^2 f(r) \left( f(r) x'(r)^2+1\right) ^{5/2}}\\ {{{\mathcal {K}}}}_{12} &= \frac{x'(r) \left( -r f'(r) x'(r)+2 f(r)^2 x'(r)^3+2 f(r) \left( x'(r)-r x''(r)\right) \right) }{2 r^2 \left( f(r) x'(r)^2+1\right) ^{5/2}}\\ {{{\mathcal {K}}}}_{21} &= \frac{x'(r) \left( -r f'(r) x'(r)+2 f(r)^2 x'(r)^3+2 f(r) \left( x'(r)-r x''(r)\right) \right) }{2 r^2 \left( f(r) x'(r)^2+1\right) ^{5/2}}\\ {{{\mathcal {K}}}}_{22} &= \frac{f(r) x'(r)^2 \left( -r f'(r) x'(r)+2 f(r)^2 x'(r)^3+2 f(r) \left( x'(r)-r x''(r)\right) \right) }{2 r^2 \left( f(r) x'(r)^2+1\right) ^{5/2}}\\ {{{\mathcal {K}}}}_{33} &= \frac{f(r) x'(r)}{r^2 \sqrt{f(r) x'(r)^2+1}}\\ {{{\mathcal {K}}}}_{44} &= \frac{f(r) x'(r)}{r^2 \sqrt{f(r) x'(r)^2+1}} \end{aligned}$$

and also one finds

$$\begin{aligned}&{R_{\mu \nu }}n_i^\mu n_i^\nu \\&\quad =\frac{r f'(r)-4 f(r)}{f(r) x'(r)^2+1}\\&\qquad -\frac{f(r) x'(r)^2 \left( r^2 f''(r)-5 r f'(r)+8 f(r)\right) }{2 \left( f(r) x'(r)^2+1\right) }\\&\qquad +\frac{1}{2} \left( -r \left( r f''(r)-5 f'(r)\right) -8 f(r)\right) \\&{R_{\mu \nu \alpha \beta }}n_i^\mu n_i^\alpha n_j^\nu n_j^\beta \\&\quad =-2 \left( \frac{f(r) x'(r)^2 \left( r^2 f''(r)-2 r f'(r)+2 f(r)\right) }{2 \left( f(r) x'(r)^2+1\right) }\right. \\&\qquad \left. -\frac{r f'(r)-2 f(r)}{2 \left( f(r) x'(r)^2+1\right) }\right) \end{aligned}$$

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Bagheri, H., Tanhayi, M.R. Higher-curvature corrections to holographic mutual information. J Theor Appl Phys (2020). https://doi.org/10.1007/s40094-020-00367-4

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Keywords

  • Holographic mutual information
  • Higher-curvature correction