Infinite conformal symmetry of critical fluctuations in two dimensions
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We study the massless quantum field theories describing the critical points in two dimensional statistical systems. These theories are invariant with respect to the 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. Exactly solvable theories associated with degenerate representations are analized. In these theories the anomalous dimensions are known exactly and the correlation functions satisfy the system of linear differential equations.
Key wordsSecond order phase transitions two-dimensional systems operator algebra conformal symmetry Vivasoro algebra Kac formula
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