Advertisement

Entanglement entropy of compactified branes and phase transition

  • Wung-Hong HuangEmail author
Research Article
  • 7 Downloads

Abstract

We first calculate the holographic entanglement entropy of M5 branes on a circle and see that it has a phase transition when decreasing the compactified radius. In particular, it is shown that the entanglement entropy scales as \(N^3\). Next, we investigate the holographic entanglement entropy of a \(D0+D4\) system on a circle and see that it scales as \(N^2\) at low energy, as in gauge theory with instantons. However, at high energy it transforms to a phase that scales as \(N^3\), as an M5 brane system. We also present the general form of holographic entanglement entropy of Dp, \(D_p+D_{p+4}\) and M-branes on a circle and see some simple relations among them. Finally, we present an analytic method to prove that they all have phase transitions from connected to disconnected surfaces as one increases the line segment that divides the entangling regions.

Keywords

Holographic entanglement entropy M5 branes D branes 

Notes

References

  1. 1.
    Hooft, Gt.: On the quantum structure of a black hole. Nucl. Phys. B 256, 727 (1985)Google Scholar
  2. 2.
    Bombelli, L., Koul, R.K., Lee, J.H., Sorkin, R.D.: A quantum source of entropy for black holes. Phys. Rev. D 34, 373 (1986)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Srednicki, M.: Entropy and area. Phys. Rev. Lett. 71, 666 (1993). arXiv:hep-th/9303048 ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Calabrese, P., Cardy, J.L.: Entanglement entropy and quantum eld theory. J. Stat. Mech. 0406, 06002 (2004). arXiv:hep-th/0405152 CrossRefGoogle Scholar
  5. 5.
    Calabrese, P., Cardy, J.L.: Entanglement entropy and quantum field theory: A non-technical introduction. Int. J. Quant. Inf. 4, 429 (2006). arXiv:quant-ph/0505193 CrossRefGoogle Scholar
  6. 6.
    Calabrese, P., Cardy, J.L.: Entanglement entropy and conformal eld theory. J. Phys. A 42, 504005 (2009). arXiv:0905.4013 [hep-th]MathSciNetCrossRefGoogle Scholar
  7. 7.
    Amico, L., Fazio, R., Osterloh, A., Vedral, V.: Entanglement in many-body systems. Rev. Mod. Phys. 80, 517 (2008). arXiv:quant-ph/0703044 ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Eisert, J., Cramer, M., Plenio, M.B.: Area laws for the entanglement entropy: a review. Rev. Mod. Phys. 82, 277 (2010). arXiv:0808.3773 [quant-ph]ADSCrossRefGoogle Scholar
  9. 9.
    Kitaev, A., Preskill, J.: Topological entanglement entropy. Phys. Rev. Lett. 96, 110404 (2006). arXiv:hep-th/0510092 ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Van Raamsdonk, M.: Comments on quantum gravity and entanglement. arXiv:0907.2939 [hep-th]
  11. 11.
    Van Raamsdonk, M.: Building up spacetime with quantum entanglement. Gen. Relativ. Gravit. 42, 2323 (2010). arXiv:1005.3035 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    Myers, R.C., Pourhasan, R., Smolkin, M.: On spacetime entanglement. JHEP 1306, 013 (2013). arXiv:1304.2030 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Balasubramanian, V., Czech, B., Chowdhury, B.D., de Boer, J.: The entropy of a hole in spacetime. JHEP 1310, 220 (2013). arXiv:1305.0856 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009). arXiv:quant-ph/0702225 ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Maldacena, J.M.: The large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2, 231 (1998). [Int. J. Theor. Phys. 38, 1113 (1999)] arXiv:hep-th/9711200
  16. 16.
    Gubser, S.S., Klebanov, I.R., Polyakov, A.M.: Gauge theory correlators from noncritical string theory. Phys. Lett. B 428, 105 (1998). arXiv:hep-th/9802109 ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    Witten, E.: Anti-de Sitter space and holography. Adv. Theor. Math. Phys. 2, 253 (1998). arXiv:hep-th/9802150 ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    Ryu, S., Takayanagi, T.: Holographic derivation of entanglement entropy from AdS/CFT. Phys. Rev. Lett. 96, 181602 (2006). arXiv:hep-th/0603001 ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    Ryu, S., Takayanagi, T.: Aspects of holographic entanglement entropy. JHEP 0608, 045 (2006). arXiv:hep-th/0605073 ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    Takayanagi, T.: Entanglement entropy from a holographic viewpoint. Class. Quant. Grav. 29, 153001 (2012). arXiv:1204.2450 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    Fursaev, D.V.: Proof of the holographic formula for entanglement entropy. JHEP 0609, 018 (2006). arXiv:hep-th/0606184 ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Lewkowycz, A., Maldacena, J.: Generalized gravitational entropy. JHEP 1308, 090 (2013). arXiv:1304.4926 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    Casini, H., Huerta, M., Myers, R.C.: Towards a derivation of holographic entanglement entropy. JHEP 1105, 036 (2011). arXiv:1102.0440 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    Nishioka, T.: Entanglement entropy: holography and renormalization group. Rev. Mod. Phys. 90, 035007 (2018). arXiv:1801.10352 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    Albash, T., Johnson, C.V.: Holographic Studies of Entanglement Entropy in Superconductors. JHEP 1205, 079 (2012). arXiv:1202.2605 [hep-th]ADSCrossRefGoogle Scholar
  26. 26.
    Cai, R.G., He, S., Li, L., Zhang, Y.L.: Holographic entanglement entropy in insulator/superconductor transition. JHEP 1207, 088 (2012). arXiv:1203.6620 [hep-th]ADSCrossRefGoogle Scholar
  27. 27.
    Klebanov, I.R., Kutasov, D., Murugan, A.: Entanglement as a probe of confinement. Nucl. Phys. B 796, 274 (2008). arXiv:0709.2140 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    Hartnoll, S.A., Radicevic, D.: Holographic order parameter for charge fractionalization. Phys. Rev. D 86, 066001 (2012). arXiv:1205.5291 [hep-th]ADSCrossRefGoogle Scholar
  29. 29.
    Pakman, A., Parnachev, A.: Topological entanglement entropy and holography. JHEP 0807, 097 (2008). arXiv:0805.1891 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    Ben-Ami, O., Carmi, D., Sonnenschein, J.: Holographic entanglement entropy of multiple strips. JHEP 11, 144 (2014). arXiv:1409.6305 [hep-th]ADSCrossRefGoogle Scholar
  31. 31.
    Renyi, A.: On measures of information and entropy. In: Procedings of the Fourth Berkeley Symposium on Mathematics, Statistics and Probability, vol. 1, p. 547 (1961)Google Scholar
  32. 32.
    Headrick, M.: Entanglement Renyi entropies in holographic theories. Phys. Rev. D 82, 126010 (2010). arXiv:1006.0047 [hep-th]ADSCrossRefGoogle Scholar
  33. 33.
    Klebanov, I.R., Pufu, S.S., Sachdev, S., Safdi, B.R.: Renyi entropies for free field theories. JHEP 1204, 074 (2012). arXiv:1111.6290 [hep-th]ADSCrossRefGoogle Scholar
  34. 34.
    Fursaev, D.V.: Entanglement Renyi entropies in conformal field theories and holography. JHEP 1205, 080 (2012). arXiv:1201.1702 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    Hung, L.Y., Myers, R.C., Smolkin, M., Yale, A.: Holographic calculations of Renyi entropy. JHEP 1112, 047 (2011). arXiv:1110.1084 [hep-th]ADSCrossRefGoogle Scholar
  36. 36.
    Belin, A., Maloney, A., Matsuura, S.: Holographic phases of Renyi entropies. JHEP 1312, 050 (2013). arXiv:1306.2640 [hep-th]ADSCrossRefGoogle Scholar
  37. 37.
    Belin, A., Hung, L.Y., Maloney, A., Matsuura, S., Myers, R.C., Sierens, T.: Holographic charged Renyi entropies. JHEP 1312, 059 (2013). arXiv:1310.4180 [hep-th]ADSCrossRefGoogle Scholar
  38. 38.
    Belin, A., Hung, L.Y., Maloney, A., Matsuuras, S.: Charged Renyi entropies and holographic superconductors. JHEP 1501, 059 (2015). arXiv:1407.5630 [hep-th]ADSCrossRefGoogle Scholar
  39. 39.
    Gubser, S.S., Klebanov, I.R., Peet, A.W.: Entropy and temperature of black 3-branes. Phys. Rev. D 54, 3915 (1996). arXiv:hep-th/9602135 ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    Klebanov, I.R., Tseytlin, A.A.: Entropy of near-extremal black p-branes. Nucl. Phys. B 475, 164 (1996). arXiv:hep-th/9604089 ADSMathSciNetCrossRefGoogle Scholar
  41. 41.
    Douglas, M.R.: On D=5 super Yang–Mills theory and (2,0) theory. JHEP 1102, 011 (2011). arXiv:1012.2880 [hep-th]ADSMathSciNetzbMATHGoogle Scholar
  42. 42.
    Lambert, N., Papageorgakis, C., Schmidt-Sommerfeld, M.: M5-branes, D4-branes and quantum 5D super-Yang–Mills. JHEP 1101, 083 (2011). arXiv:1012.2882 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    Quijada, E., Boschi-Filho, H.: Entanglement entropy for D3-, M2- and M5-brane backgrounds. arXiv:1711.08505 [hep-th]

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of PhysicsNational Cheng Kung UniversityTainanTaiwan

Personalised recommendations