Skip to main content

Introduction to Gauge/Gravity Duality

  • Chapter
  • First Online:
Strings and Fundamental Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 851))

Abstract

The AdS/CFT correspondence and its generalizations to gauge/gravity duality are a major recent development within theoretical physics. We begin these lectures with an overview over the prerequisites necessary for understanding the correspondence. Then we move on to discussing the AdS/CFT correspondence itself, as well as giving an important test of the conjectured duality. Finally, as an example for gauge/gravity duality, we discuss the case of finite temperature and density, which is the starting point for many applications.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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. 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 (1999) 1113][arXiv:hep-th/9711200]

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  4. Freedman, D.Z., Mathur, S.D., Matusis, A., Rastelli, L.: Correlation functions in the CFT \((d)/\hbox{AdS}(d+1)\) correspondence. Nucl. Phys. B 546, 96 (1999) [arXiv:hep-th/9804058]

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. 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:hep-th/9905111]

    Article  MathSciNet  ADS  Google Scholar 

  6. D’Hoker, E., Freedman, D.Z.: Supersymmetric gauge theories and the AdS/CFT correspondence, arXiv:hep-th/0201253

    Google Scholar 

  7. Petersen, J.L.: Introduction to the Maldacena conjecture on AdS/CFT. Int. J. Mod. Phys. A 14, 3597 (1999) [arXiv:hep-th/9902131]

    Article  ADS  MATH  Google Scholar 

  8. Maldacena, J.: The gauge/gravity duality, [arXiv:1106.6073 [hep-th]]

    Google Scholar 

  9. Son, D.T., Starinets, A.O.: Viscosity, Black Holes, and Quantum Field Theory. Ann. Rev. Nucl. Part. Sci. 57, 95–118 (2007) [arXiv:0704.0240 [hep-th]]

    Article  ADS  Google Scholar 

  10. Erdmenger, J., Evans, N., Kirsch, I., Threlfall, E.: Mesons in Gauge/Gravity Duals - A Review. Eur. Phys. J. A 35, 81–133 (2008) [arXiv:0711.4467 [hep-th]]

    Article  ADS  Google Scholar 

  11. Hartnoll, S.A.: Lectures on holographic methods for condensed matter physics. Class. Quant. Grav. 26, 224002 (2009) [arXiv:0903.3246 [hep-th]]

    Article  MathSciNet  ADS  Google Scholar 

  12. Herzog, C.P.: Lectures on Holographic Superfluidity and Superconductivity. J. Phys. A A42, 343001 (2009) [arXiv:0904.1975 [hep-th]]

    Article  Google Scholar 

  13. Osborn, H., Petkou, A.C.: Implications of conformal invariance in field theories for general dimensions. Annals Phys. 231, 311–362 (1994) [hep-th/9307010]

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Erdmenger, J., Osborn, H.: Conserved Currents and the Energy Momentum Tensor in Conformally Invariant Theories for General Dimensions. Nucl. Phys. B 483, 431–474 (1997) [arXiv:hep-th/9605009]

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. Coleman, S.: Aspects of Symmetry, Selected Erice Lectures. Cambridge University Press, Cambridge (1988)

    Google Scholar 

  16. Lee, S., Minwalla, S., Rangamani, M., Seiberg, N.: Three point functions of chiral operators in D = 4, N=4 SYM at large N. Adv. Theor. Math. Phys. 2, 697–718 (1998) [hep-th/9806074]

    MathSciNet  MATH  Google Scholar 

  17. D’Hoker, E., Freedman, D.Z., Skiba, W.: Field theory tests for correlators in the AdS / CFT correspondence. Phys. Rev. D 59, 045008 (1999) [hep-th/9807098]

    Article  MathSciNet  ADS  Google Scholar 

  18. D’Hoker, E., Freedman, D.Z., Mathur, S.D., Matusis, A., Rastelli, L.: Extremal correlators in the AdS / CFT correspondence, In: Shifman, M.A. (ed.) The many faces of the superworld, pp. 332–360 [hep-th/9908160]

    Google Scholar 

  19. Erdmenger, J., Pérez-Victoria, M.: Nonrenormalization of next-to-extremal correlators in N=4 SYM and the AdS / CFT correspondence. Phys. Rev. D 62, 045008 (2000) [hep-th/9912250]

    Article  MathSciNet  ADS  Google Scholar 

  20. Kim, H.J., Romans, L.J., van Nieuwenhuizen, P.: The Mass Spectrum of Chiral \({\fancyscript{N}}c=2,\) \(D\,=\,10\) Supergravity on \(S^5.\) Phys. Rev. D 32, 389 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  21. Beisert, N., Ahn, C., Alday, L.F., Bajnok, Z., Drummond, J.M., Freyhult, L., Gromov, N., Janik, R.A., et al.: Review of AdS/CFT integrability: An overview [arXiv:1012.3982 (hep-th)]

    Google Scholar 

Download references

Acknowledgements

I am grateful to Martin Ammon, to Hai Ngo and to Oliver Schlotterer for help with preparing this manuscript. Moreover I would like to thank my tutors at the school, Martin Ammon, Viviane Grass, Shu Lin, Hai Ngo and Andy O’Bannon.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Johanna Erdmenger .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Erdmenger, J. (2012). Introduction to Gauge/Gravity Duality. In: Baumgartl, M., Brunner, I., Haack, M. (eds) Strings and Fundamental Physics. Lecture Notes in Physics, vol 851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25947-0_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-25947-0_3

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25946-3

  • Online ISBN: 978-3-642-25947-0

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics