# Belavin, Polyakov, Zamolodchikov ## Infinite conformal symmetry in two-dimensional quantum field theory \[Links: [DOI](https://doi.org/10.1016/0550-3213(84)90052-X)\] \[Abstract: We present an investigation of the massless, two-dimentional, interacting field theories. Their basic property is their invariance under an infinite-dimensional group of conformal (analytic) transformations. It is shown that the local fields forming the operator algebra can be classified according to the irreducible representations of [[0032 Virasoro algebra|Virasoro algebra]], and that the correlation functions are built up of the “[[0031 Conformal block|conformal blocks]]” which are completely determined by the [[0028 Conformal symmetry|conformal invariance]]. Exactly solvable conformal theories associated with the degenerate representations are analyzed. In these theories the anomalous dimensions are known exactly and the correlation functions satisfy the systems of linear differential equations.\] # Cardy ## Conformal invariance and surface critical behavior \[Links: [Inspire](https://inspirehep.net/literature/209563), [DOI](https://doi.org/10.1016/0550-3213(84)90241-4)\] \[Abstract: Conformal invariance constrains the form of correlation functions near a free surface. In two dimensions, for a wide class of models, it completely determines the correlation functions at the critical point, and yields the exact values of the surface critical exponents. They are related to the bulk exponents in a non-trivial way. For the $Q$-state Potts model $(0 \le Q\le 4)$ we find $\eta_{||}= 2(3v − 1)$, and for the $O(N)$ model $(−2\le N\le2)$, $\eta_{||}=(2v−1)(4v−1)$.\]