Abstract
This is a pedagogical introduction to the AdS/CFT correspondence. Starting with the conceptual basis of the holographic dualities, the subject is developed emphasizing some concrete topics, which are discussed in detail. A very brief introduction to string theory is provided, containing the minimal ingredients to understand the origin of the AdS/CFT duality. Other topics covered are the holographic calculation of correlation functions, quark–antiquark potentials and transport coefficients.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
J.M. Maldacena, The large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2, 231 (1998). arXiv:hep-th/9711200
S.S. Gubser, I.R. Klebanov, A.M. Polyakov, Gauge theory correlators from noncritical string theory. Phys. Lett. B 428, 105 (1998). arXiv:hep-th/9802109
E. Witten, Anti-de Sitter space and holography. Adv. Theor. Math. Phys. 2, 253 (1998). arXiv:hep-th/9802150
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri, Y. Oz, Large N field theories, string theory and gravity. Phys. Rep. 323, 183 (2000). arXiv:hep-th/9905111
E. D’Hoker, D.Z. Freedman, Supersymmetric gauge theories and the AdS/CFT correspondence, in Strings, Brane and extra dimensions: TASI 2001, ed. by StevenS. Gubser, Joseph D. Lykken (River Edge, N.J., World Scientific, 2004) arXiv:hep-th/0201253
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics. Class. Quantum Gravity 26, 224002 (2009). arXiv:0903.3246 [hep-th]
J. McGreevy, Holographic duality with a view toward many-body physics. Adv. High Energy Phys. 2010, 723105 (2010). arXiv:0909.0518 [hep-th]
J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal, U.A. Wiedemann, Gauge/string duality, hot QCD and heavy Ion collisions. (Cambridge University Press, Cambridge, UK, 2014)
Y. Kim, I.J. Shin, T. Tsukioka, Holographic QCD: past, present, and future. Prog. Part. Nucl. Phys. 68, 55 (2013). arXiv:1205.4852 [hep-ph]
A. Adams, L.D. Carr, T. Schäfer, P. Steinberg, J.E. Thomas, Strongly correlated quantum fluids: ultracold quantum gases, quantum chromodynamic plasmas, and holographic duality. New J. Phys. 14, 115009 (2012). arXiv:1205.5180 [hep-th]
M.B. Green, J.H. Schwarz, E. Witten, Superstring Theory, vol. 2 (Cambridge University Press, Cambridge, 1987)
J. Polchinski, String Theory, vol. 2 (Cambridge University Press, Cambridge, 1998)
K. Becker, M. Becker, J.H. Schwarz, String Theory and M-Theory (Cambridge University Press, Cambridge, 2007)
E. Kiritsis, String Theory in a Nutshell (Princeton University Press, Princeton, 2007)
B. Zwiebach, A First Course in String Theory (Cambridge University Press, Cambridge, 2009)
L.E. Ibañez, A. Uranga, String Theory and Particle Physics (Cambridge University Press, Cambridge, 2012)
G. ’t Hooft, A planar diagram theory for strong interactions. Nucl. Phys. B 72, 461 (1974)
A.V. Manohar, Large N QCD. in Probing the Standard Model of Particle Interactions, ed. by R. Gupta, A. Morel, E. De Rafael, F. David. Amsterdam, (Elsevier, The Netherlands, 1999) arXiv:hep-ph/9802419
M. Henningson, K. Skenderis, The holographic Weyl anomaly. JHEP 9807, 023 (1998). arXiv:hep-th/9806087
S. de Haro, S.N. Solodukhin, K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence. Commun. Math. Phys. 217, 595 (2001). arXiv:hep-th/0002230
K. Skenderis, Lecture notes on holographic renormalization. Class. Quantum Gravity 19, 5849 (2002). arXiv:hep-th/0209067
J.M. Maldacena, Wilson loops in large N field theories. Phys. Rev. Lett. 80, 4859 (1998). arXiv:hep-th/9803002
S.J. Rey, J.T. Yee, Macroscopic strings as heavy quarks in large N gauge theory and anti-de Sitter supergravity. Eur. Phys. J. C 22, 379 (2001). arXiv:hep-th/9803001
P. Kovtun, D.T. Son, A.O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics. Phys. Rev. Lett. 94, 111601 (2005). arXiv:hep-th/0405231
D.T. Son, A.O. Starinets, Viscosity, black holes, and quantum field theory. Ann. Rev. Nucl. Part. Sci. 57, 95 (2007). arXiv:0704.0240 [hep-th]
J. Erdmenger, N. Evans, I. Kirsch, E. Threlfall, Mesons in gauge/gravity duals—a review. Eur. Phys. J. A 35, 81 (2008). arXiv:0711.4467 [hep-th]
J.D. Edelstein, R. Portugues, Gauge/string duality in confining theories. Fortsch. Phys. 54, 525 (2006). arXiv:hep-th/0602021
K. Peeters, M. Zamaklar, The string/gauge theory correspondence in QCD. Eur. Phys. J. ST 152, 113 (2007). arXiv:0708.1502 [hep-th]
D. Mateos, String theory and quantum chromodynamics. Class. Quantum Gravity 24, S713 (2007). arXiv:0709.1523 [hep-th]
M. Piai, Lectures on walking technicolor, holography and gauge/gravity dualities. Adv. High Energy Phys. 2010, 464302 (2010). arXiv:1004.0176 [hep-ph]
N. Beisert, C. Ahn, L.F. Alday, Z. Bajnok, J.M. Drummond, L. Freyhult, N. Gromov, R.A. Janik et al., Review of AdS/CFT integrability: an overview. Lett. Math. Phys. 99, 3 (2012). arXiv:1012.3982 [hep-th]
S. Sachdev, Condensed matter and AdS/CFT. Lect. Notes Phys. 828, 273 (2011). arXiv:1002.2947 [hep-th]
S. Sachdev, What can gauge-gravity duality teach us about condensed matter physics? Ann. Rev. Condens. Matter Phys. 3, 9 (2012). arXiv:1108.1197 [cond-mat.str-el]
A.G. Green, An introduction to gauge gravity duality and its application in condensed matter. Contemp. Phys. 54(01), 33–48 (2013). arXiv:1304.5908 [cond-mat.str-el]
T. Nishioka, S. Ryu, T. Takayanagi, Holographic entanglement entropy: an overview. J. Phys. A 42, 504008 (2009). arXiv:0905.0932 [hep-th]
T. Takayanagi, Entanglement entropy from a holographic viewpoint. Class. Quantum Gravity 29, 153001 (2012). arXiv:1204.2450 [gr-qc]
M. Rangamani, Gravity and hydrodynamics: lectures on the fluid-gravity correspondence. Class. Quantum Gravity 26, 224003 (2009). arXiv:0905.4352 [hep-th]
V.E. Hubeny, S. Minwalla, M. Rangamani, The fluid/gravity correspondence in String Theory and Its Applications: From meV to the Planck Scale, ed. by M. Dine, T. Banks, S. Sachdev, (World Scientific, 2012) arXiv:1107.5780 [hep-th]
Acknowledgments
I am grateful to Yago Bea, Niko Jokela, Javier Mas and Ricardo Vázquez for their comments and help in the preparation of these lecture notes. I also thank Carlos Merino for his invitation to deliver the course on the AdS/CFT correspondence at the third IDPASC school. This work is funded in part by the Spanish grant FPA2011-22594, by Xunta de Galicia (Consellería de Educación, grant INCITE09 206 121 PR and grant PGIDIT10PXIB206075PR), by the Consolider-Ingenio 2010 Programme CPAN (CSD2007-00042), and by FEDER.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Ramallo, A.V. (2015). Introduction to the AdS/CFT Correspondence. In: Merino, C. (eds) Lectures on Particle Physics, Astrophysics and Cosmology. Springer Proceedings in Physics, vol 161. Springer, Cham. https://doi.org/10.1007/978-3-319-12238-0_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-12238-0_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12237-3
Online ISBN: 978-3-319-12238-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)