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.
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References
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]
Witten, E.: Anti-de sitter space and holography. Adv. Theor. Math. Phys. 2, 253 (1998) [arXiv:hep-th/9802150]
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]
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]
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]
D’Hoker, E., Freedman, D.Z.: Supersymmetric gauge theories and the AdS/CFT correspondence, arXiv:hep-th/0201253
Petersen, J.L.: Introduction to the Maldacena conjecture on AdS/CFT. Int. J. Mod. Phys. A 14, 3597 (1999) [arXiv:hep-th/9902131]
Maldacena, J.: The gauge/gravity duality, [arXiv:1106.6073 [hep-th]]
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]]
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]]
Hartnoll, S.A.: Lectures on holographic methods for condensed matter physics. Class. Quant. Grav. 26, 224002 (2009) [arXiv:0903.3246 [hep-th]]
Herzog, C.P.: Lectures on Holographic Superfluidity and Superconductivity. J. Phys. A A42, 343001 (2009) [arXiv:0904.1975 [hep-th]]
Osborn, H., Petkou, A.C.: Implications of conformal invariance in field theories for general dimensions. Annals Phys. 231, 311–362 (1994) [hep-th/9307010]
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]
Coleman, S.: Aspects of Symmetry, Selected Erice Lectures. Cambridge University Press, Cambridge (1988)
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]
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]
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]
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]
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)
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)]
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.
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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
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