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==Two-dimensional case==
[[Alexander Zamolodchikov]] proved in 1986 that two-dimensional quantum field theory always has such a ''C''-function. Moreover, at fixed points of the RG flow, which correspond to [[two-dimensional conformal field theory|conformal field theories]], Zamolodchikov's ''C''-function is equal to the [[central charge]] of the corresponding conformal field theory,<ref>{{cite journal | last1 = Zamolodchikov | first1 = A. B. | authorlink = Alexander Zamolodchikov | year = 1986 | title = "Irreversibility" of the Flux of the Renormalization Group in a 2-D Field Theory | url = http://www.jetpletters.ac.ru/ps/1413/article_21504.pdf | format = PDF | journal = JETP Lett | volume = 43 | issue = | pages = 730–732 }}</ref> which lends the name ''C'' to the theorem.
==Four-dimensional case: ''A''-theorem==
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