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Infinite conformal symmetry in two-dimensional quantum field theory. (English) Zbl 0661.17013
We present an investigation of the massless, two-dimensional, interacting field theories. Their basic property is their invariance under an infinite-dimensional group of conformal (analytic) transformations. It is shown that the local fields forming the operator algebra can be classified according to the irreducible representations of the Virasoro algebra, and that the correlation functions are built up of the ‘conformal blocks’ which are completely determined by the conformal invariance. Exactly solvable conformal theories associated with the degenerate representations are analyzed. In these theories the anomalous dimensions are known exactly and the correlation functions satisfy systems of linear differential equations.

MSC:
17B65 Infinite-dimensional Lie (super)algebras
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
58J90 Applications of PDEs on manifolds
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
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[1] Patashinskii, A.Z.; Pokrovskii, V.L., Fluctuation theory of phase transitions, (1979), Pergamon Oxford
[2] Polyakov, A.M., Zhetf lett., 12, 538, (1970)
[3] Migdal, A.A., Phys. lett., 44B, 112, (1972)
[4] Polyakov, A.M., Zhetf, 66, 23, (1974)
[5] Wilson, K.G., Phys. rev., 179, 1499, (1969)
[6] Feigin, B.L.; Fuks, D.B., Funktz. analiz, 16, 47, (1982)
[7] Kac, V.G., Lecture notes in phys., 94, 441, (1979)
[8] Mandelstam, S., Phys. reports, 12C, 1441, (1975)
[9] Schwarz, J.H., Phys. reports, 8C, 269, (1973)
[10] Gelfand, I.M.; Fuks, D.B., Funktz. analiz, 2, 92, (1968)
[11] Virasoro, M., Phys. rev., D1, 2933, (1969)
[12] Bateman, H.; Erdelyi, A., Higher transcendental functions, (1953), McGraw-Hill
[13] Poincaré, A., ()
[14] Polyakov, A.M., Phys. lett., 103B, 207, (1981)
[15] McKoy, B.; Wu, T.T., The two-dimensional Ising model, (1973), Harvard Univ. Press
[16] Luther, A.; Peschel, I., Phys. rev., B12, 3908, (1975)
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