Abstract
In this chapter, we shall describe an overall picture of the AdS/CFT duality. Many terms appear below, but we will explain each in later chapters, so readers should not worry about them too much for the time being.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The gauge theory is often called the “boundary theory” whereas the gravitational theory is called the “bulk theory.”
- 2.
Normally, one would not use the word “weakly-coupled gravity,” but this means that the spacetime curvature is small. The gravitational theory satisfies this condition when the gauge theory is strongly-coupled. Conversely, when the gravitational theory is strongly-coupled in the above sense, the gauge theory is weakly-coupled.
- 3.
Note that \({\fancyscript{N}}\) denotes the number of supersymmetry whereas \(N_c\) denotes the number of “colors” in the \(\textit{SU}(N_c)\) gauge theory.
- 4.
Since the name AdS/CFT is not really appropriate, various alternative names have been proposed. The name “holographic theory” is one of them. The other strong candidate is the “gauge/gravity duality,” but this name becomes inconvenient since one started to apply AdS/CFT not only to QCD but to field theory in general. One may see phrases such as “bulk/boundary duality” or “field theory/gravity duality.” The name “gauge/string duality” is adopted in the PACS (Physics and Astronomy Classification Scheme) code by American Institute of Physics. This name is also appropriate since the dual of a gauge theory is really a string theory as we will see later. Anyway, they all mean the same. In this book, we use the most common name “AdS/CFT duality” without making a new name since it is not clear at this moment how far AdS/CFT will be applied. A digression: AdS/CFT keeps having troubles with name from the beginning. It was originally called the “Maldacena’s conjecture.” But it is common that a duality is hard to prove and first starts as a conjecture, so the name became obsolete.
- 5.
QCD is a \(\textit{SU}(3)\) gauge theory, but AdS/CFT typically considers a \(\textit{SU}(N_c)\) supersymmetric gauge theory, so one should note that AdS/CFT gives only approximate results.
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
C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (W.H. Freeman, New York, 1973)
O. Aharony, S.S. Gubser, J. Maldacena, H. Ooguri, Y. Oz, Large N field theories, string theory and gravity. Phys. Rep. 323, 183 (2000). arXiv:hep-th/9905111
M.B. Green, J.H. Schwarz, E. Witten, Superstring Theory (Cambridge University Press, Cambridge, 1987)
J. Polchinski, String Theory (Cambridge University Press, Cambridge, 1998)
B. Zwiebach, A First Course in String Theory, 2nd edn. (Cambridge University Press, Cambridge, 2009)
K. Becker, M. Becker, J.H. Schwarz, String Theory and M-theory: A Modern Introduction (Cambridge University Press, Cambridge, 2007)
E. Kiritsis, String Theory in a Nutshell (Princeton University Press, Princeton, 2007)
C.V. Johnson, D-branes (Cambridge University Press, Cambridge, 2003)
B.F. Schutz, A First Course in General Relativity, 2nd edn. (Cambridge University Press, Cambridge, 2009)
A. Zee, Einstein Gravity in a Nutshell (Princeton University Press, Princeton, 2013)
R.M. Wald, General Relativity (University of Chicago Press, Chicago, 1984)
E. Papantonopoulos (ed.), From Gravity to Thermal Gauge Theories: The AdS/CFT Correspondence. Lecture Notes in Physics, vol. 828 (Springer, Berlin, 2011)
G. Horowitz (ed.), Black Holes in Higher Dimensions (Cambridge University Press, Cambridge, 2012)
J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal, U.A. Wiedemann, Gauge/string duality, hot QCD and heavy ion collisions. arXiv:1101.0618 [hep-th]
O. DeWolfe, S.S. Gubser, C. Rosen, D. Teaney, Heavy ions and string theory. arXiv:1304.7794 [hep-th]
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]
N. Iqbal, H. Liu, M. Mezei, Lectures on holographic non-Fermi liquids and quantum phase transitions. arXiv:1110.3814 [hep-th]
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Springer Japan
About this chapter
Cite this chapter
Natsuume, M. (2015). Introduction. In: AdS/CFT Duality User Guide. Lecture Notes in Physics, vol 903. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55441-7_1
Download citation
DOI: https://doi.org/10.1007/978-4-431-55441-7_1
Published:
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-55440-0
Online ISBN: 978-4-431-55441-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)