Skip to main content

Emergence of Gravity and RG Flow

  • Chapter
  • First Online:
Gravity and the Quantum

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 187))

  • 1811 Accesses

Abstract

This is a tribute to Padmanabhan’s works on the holographic principle which have consistently enunciated the profound philosophy that the classical equations of gravity themselves hold the key to understanding their holographic origin. I discuss how this can be realised by reformulating Einstein’s equations in AdS as a non-perturbative RG flow that further leads to a new approach towards constructing strongly interacting QFTs. For a concrete demonstration, I focus on the hydrodynamic limit in which case this RG flow connects the AdS/CFT correspondence with the membrane paradigm.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. G. ’t Hooft, The Holographic principle: opening lecture. Subnucl. Ser. 37, 72–100 (2001). arXiv:hep-th/0003004

    Google Scholar 

  2. L. Susskind, The World as a hologram. J. Math. Phys. 36, 6377–6396 (1995). arXiv:hep-th/9409089

  3. R. Bousso, The Holographic principle. Rev. Mod. Phys. 74, 825–874 (2002). arXiv:hep-th/0203101

    Article  ADS  MATH  MathSciNet  Google Scholar 

  4. J.M. Maldacena, TASI 2003 lectures on AdS/CFT, in Progress in String Theory. Proceedings, Summer School, TASI 2003, Boulder, USA, 2–27 June 2003 (2003), pp. 155–203. arXiv:hep-th/0309246

  5. J.M. Maldacena, The large N limit of superconformal field theories and supergravity. Int. J. Theor. Phys. 38, 1133 (1999). arXiv:hep-th/9711200

  6. E. Witten, Anti-de Sitter space and holography. Adv. Theor. Math. Phys. 2, 253–291 (1998). arXiv:hep-th/9802150

  7. S. Gubser, I.R. Klebanov, A.M. Polyakov, Gauge theory correlators from noncritical string theory. Phys. Lett. B 428, 105–114 (1998). arXiv:hep-th/9802109

  8. T. Padmanabhan, The Holography of gravity encoded in a relation between entropy, horizon area and action for gravity. Gen. Rel. Grav. 34, 2029–2035 (2002). arXiv:gr-qc/0205090

    Article  ADS  MATH  MathSciNet  Google Scholar 

  9. T. Padmanabhan, Gravitational entropy of static space-times and microscopic density of states. Class. Quant. Grav. 21, 4485–4494 (2004). arXiv:gr-qc/0308070

    Article  ADS  MATH  Google Scholar 

  10. T. Padmanabhan, Holographic gravity and the surface term in the Einstein–Hilbert action. Braz. J. Phys. 35, 362–372 (2005). arXiv:gr-qc/0412068

    Article  ADS  Google Scholar 

  11. A. Mukhopadhyay, T. Padmanabhan, Holography of gravitational action functionals. Phys. Rev. D 74, 124023 (2006). arXiv:hep-th/0608120

  12. M. Akbar, R.-G. Cai, Thermodynamic behavior of field equations for f(R) gravity. Phys. Lett. B 648, 243–248 (2007). arXiv:gr-qc/0612089

  13. D. Kothawala, S. Sarkar, T. Padmanabhan, Einstein’s equations as a thermodynamic identity: the cases of stationary axisymmetric horizons and evolving spherically symmetric horizons. Phys. Lett. B 652, 338–342 (2007). arXiv:gr-qc/0701002

  14. T. Padmanabhan, A. Paranjape, Entropy of null surfaces and dynamics of spacetime. Phys. Rev. D 75, 064004 (2007). arXiv:gr-qc/0701003

  15. T. Padmanabhan, Thermodynamical aspects of gravity: new insights. Reports Prog. Phys. 73, 046901 (2010). arXiv:0911.5004

    Article  ADS  Google Scholar 

  16. T. Padmanabhan, Dark energy and gravity. General Relativ. Gravit. 40, 529–564 (2008). arXiv:0705.2533

    Article  ADS  MATH  MathSciNet  Google Scholar 

  17. S. Kuperstein, A. Mukhopadhyay, The unconditional RG flow of the relativistic holographic fluid. JHEP 11, 130 (2011). arXiv:1105.4530

    Article  ADS  MATH  Google Scholar 

  18. S. Kuperstein, A. Mukhopadhyay, Spacetime emergence via holographic RG flow from incompressible Navier–Stokes at the horizon. JHEP 11, 086 (2013). arXiv:1307.1367

    Article  ADS  Google Scholar 

  19. N. Behr, S. Kuperstein, A. Mukhopadhyay, Holography as a highly efficient renormalization group flow. I. Rephrasing gravity. Phys. Rev. D 94(2), 026001 (2016). arXiv:1502.06619

  20. N. Behr, A. Mukhopadhyay, Holography as a highly efficient renormalization group flow. II. An explicit construction. Phys. Rev. D 94(2), 026002 (2016). arXiv:1512.09055

  21. I.R. Klebanov, M.J. Strassler, Supergravity and a confining gauge theory: duality cascades and chi SB resolution of naked singularities. JHEP 08, 052 (2000). arXiv:hep-th/0007191

    Article  ADS  MATH  Google Scholar 

  22. G. Policastro, D.T. Son, A.O. Starinets, The shear viscosity of strongly coupled N=4 supersymmetric Yang–Mills plasma. Phys. Rev. Lett. 87, 081601 (2001). arXiv:hep-th/0104066

    Article  ADS  Google Scholar 

  23. R. Baier, P. Romatschke, D.T. Son, A.O. Starinets, M.A. Stephanov, Relativistic viscous hydrodynamics, conformal invariance, and holography. JHEP 04, 100 (2008). arXiv:0712.2451

    Article  ADS  MATH  MathSciNet  Google Scholar 

  24. S. Bhattacharyya, V.E. Hubeny, S. Minwalla, M. Rangamani, Nonlinear fluid dynamics from gravity. JHEP 02, 045 (2008). arXiv:0712.2456

    Article  ADS  Google Scholar 

  25. T. Damour, Black hole eddy currents. Phys. Rev. D 18, 3598–3604 (1978)

    Article  ADS  Google Scholar 

  26. K.S. Thorne, R.H. Price, D.A. MacDonald, Black Holes: The Membrane Paradigm (Yale University Press, New Haven, 1986)

    MATH  Google Scholar 

  27. R.K. Gupta, A. Mukhopadhyay, On the universal hydrodynamics of strongly coupled CFTs with gravity duals. JHEP 03, 067 (2009). arXiv:0810.4851

  28. I. Heemskerk, J. Polchinski, Holographic and Wilsonian renormalization groups. JHEP 06, 031 (2011). arXiv:1010.1264

  29. R.L. Arnowitt, S. Deser, C.W. Misner, The dynamics of general relativity. General Rel. Grav. 40, 1997–2027 (2008). arXiv:gr-qc/0405109

  30. A. Balcerzak, M.P. Dabrowski, Generalized Israel junction conditions for a fourth-order brane world. Phys. Rev. D 77, 023524 (2008). arXiv:0710.3670

  31. M. Henningson, K. Skenderis, Holography and the Weyl anomaly. Fortsch. Phys. 48, 125–128 (2000). arXiv:hep-th/9812032

  32. V. Balasubramanian, P. Kraus, A stress tensor for anti-de sitter gravity. Commun. Math. Phys. 208, 413–428 (1999). arXiv:hep-th/9902121

  33. J. de Boer, E.P. Verlinde, H.L. Verlinde, On the holographic renormalization group. JHEP 08, 003 (2000). arXiv:hep-th/9912012

  34. I. Bredberg, C. Keeler, V. Lysov, A. Strominger, Wilsonian approach to fluid/gravity duality. JHEP 03, 141 (2011). arXiv:1006.1902

  35. R. Penrose, W. Rindler, Spinors and Spacetime, Chap. 9, vol. 2, Spinor and Twistor Methods in Space-Time Geometry (Cambridge University Press, Cambridge, 1986)

    Book  MATH  Google Scholar 

  36. J.D. Brown, M. Henneaux, Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity. Commun. Math. Phys. 104, 207–226 (1986)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  37. A. Schwimmer, S. Theisen, Diffeomorphisms, anomalies and the Fefferman–Graham ambiguity. JHEP 0008, 032 (2000). arXiv:hep-th/0008082

  38. R. Iyer and A. Mukhopadhyay, An AdS/CFT connection between Boltzmann and Einstein. Phys. Rev. D 81, 086005 (2010). arXiv:0907.1156

  39. R. Iyer, A. Mukhopadhyay, Homogeneous relaxation at strong coupling from gravity. Phys. Rev. D 84, 126013 (2011). arXiv:1103.1814

  40. M.P. Heller, R.A. Janik, M. Spaliński, P. Witaszczyk, Coupling hydrodynamics to nonequilibrium degrees of freedom in strongly interacting quark-gluon plasma. Phys. Rev. Lett. 113(26), 261601 (2014). arXiv:1409.5087

  41. M.P. Heller, R.A. Janik, P. Witaszczyk, Hydrodynamic gradient expansion in gauge theory plasmas. Phys. Rev. Lett. 110(21), 211602 (2013). arXiv:1302.0697

  42. G. Basar, G.V. Dunne, Hydrodynamics, resurgence, and transasymptotics. Phys. Rev. D 92(12), 125011 (2015). arXiv:1509.05046

  43. T. Faulkner, M. Guica, T. Hartman, R.C. Myers, M. Van Raamsdonk, Gravitation from entanglement in holographic CFTs. JHEP 03, 051 (2014). arXiv:1312.7856

  44. S. Ryu, T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT. Phys. Rev. Lett. 96,181602 (2006). arXiv:hep-th/0603001

  45. B. Swingle, Entanglement renormalization and holography. Phys. Rev. D 86, 065007 (2012)

    Article  ADS  Google Scholar 

  46. E. Iancu, A. Mukhopadhyay, A semi-holographic model for heavy-ion collisions. JHEP 06, 003 (2015). arXiv:1410.6448

  47. A. Mukhopadhyay, F. Preis, A. Rebhan, S.A. Stricker, Semi-holography for heavy ion collisions: self-consistency and first numerical tests. JHEP 05, 141 (2016). arXiv:1512.06445

Download references

Acknowledgements

The research of A.M. is supported by a Lise-Meitner fellowship of the Austrian Science Fund (FWF), project no. M 1893-N27.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ayan Mukhopadhyay .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Mukhopadhyay, A. (2017). Emergence of Gravity and RG Flow. In: Bagla, J., Engineer, S. (eds) Gravity and the Quantum. Fundamental Theories of Physics, vol 187. Springer, Cham. https://doi.org/10.1007/978-3-319-51700-1_17

Download citation

Publish with us

Policies and ethics