Lectures: | Sergei Sibiryakov |

Sergei Demidov |

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

## Abstract

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.

## Literature

### Textbooks:

*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.

### Papers:

*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].