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Lectures:Sergei Sibiryakov
Sergei Demidov

Elements of conformal field theories and string theory (Semester 10)


Development of many branches of theoretical physics has been related to the notion of conformal invariance. The applications of conformal field theories (CFTs) range from high-energy physics to the description of critical phenomena in condensed matter. Besides, two-dimensional conformal theories lie at the foundations of the string theory that provides at present the most developed approach to quantization of gravity. Recently, it has turned out that the above theories are even closer interconnected: the string theory in certain backgrounds (similar to the so-called anti-de Sitter (AdS) spacetime) is dual to conformal field theories in dimensions higher than two. This theoretical discovery has led to the concept of the AdS/CFT duality (also called holographic duality) that currently finds numerous applications in various domains of theoretical physics. This lecture course gives an introduction to the formalism of conformal field theory and string theory with the aim to provide a necessary background for a deeper study of these disciplines and to prepare the student for understanding the ideas of holographic duality.



  • J. Polchinski, "String Theory, Volumes 1,2." Cambridge University Press, 1998.
  • P. Di Francesco, P. Mathieu, D. Senechal, "Conformal Field Theory." Springer, New York, 1997.
  • M.B. Green, J.H. Schwartz, E. Witten, "Superstring theory, vol. 1,2." Cambridge University Press, 1987.


  • A.A. Belavin, A.M. Polyakov and A.B. Zamolodchikov, "Infinite conformal symmetry in two-dimensional quantum field theory." Nucl. Phys. B 241, 333 (1984).
  • J. Polchinski, "Scale and conformal invariance in quantum field theory." Nucl. Phys. B 303, 226 (1988).
  • A.M. Polyakov, "Quantum geometry of bosonic strings." Phys. Lett. B 103, 207 (1981).
  • J.M. Maldacena, "The large N limit of superconformal field theories and supergravity," Adv. Theor. Math. Phys. 2, 231 (1998) [Int. J. Theor. Phys. 38, 1113 (1999)] [arXiv:hep-th/9711200].
  • O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, "Large N field theories, string theory and gravity." Phys. Rept. 323, 183 (2000) [arXiv:hep-th/9905111].