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2016

Minimal lectures on two-dimensional conformal field theory

Ribault, Sylvain

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We provide a brief but self-contained review of two-dimensional conformal field theory, from the basic principles to some of the simplest models.

From the representations of the Virasoro algebra on the one hand, and the state-field correspondence on the other hand, we deduce Ward identities and Belavin--Polyakov--Zamolodchikov equations for correlation functions.
We then explain the principles of the conformal bootstrap method, and introduce conformal blocks.
This allows us to define and solve minimal models and Liouville theory.

Minimal lectures on two-dimensional conformal field theory · Around

Built on

V. B. Petkova (1988) Two-dimensional (Half) Integer Spin Conformal Theories With Central Charge c < 1 c<1
1988
Earlier work this paper cites.
G. W. Moore, N. Seiberg (1989) Classical and Quantum Conformal Field Theory
1989
Earlier work this paper cites.
A. Zamolodchikov, A. Zamolodchikov (1990 book) Conformal Field Theory and Critical Phenomena in Two-Dimensional Systems
1990
Earlier work this paper cites.
A. B. Zamolodchikov, A. B. Zamolodchikov (1996) [arXiv:hep-th/9506136] Structure constants and conformal bootstrap in Liouville field theory
1996
Earlier work this paper cites.

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Then

S. Ribault, R. Santachiara (2015) [arXiv:1503.02067] Liouville theory with a central charge less than one
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2015
Later among the works it cites.
S. Migliaccio, S. Ribault (2017) [arXiv:1711.08916] The analytic bootstrap equations of non-diagonal two-dimensional CFT
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2017
Closest in time.
J. Teschner (2017 review) [arXiv:1708.00680] A guide to two-dimensional conformal field theory
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2017
Closest in time.

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