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m →Four-dimensional case - ''A''-theorem: Journal cites, added 1 PMID using AWB (12142) |
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[[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 [[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
Until recently, it had not been possible to prove an analog ''C''-theorem in higher-dimensional quantum field theory. It is known that at fixed points of the RG flow, if such function exists, it will no more be equal to the central charge {{mvar|c}}, but rather to a different quantity {{mvar|a}}.<ref>{{cite journal | last1 = Nakayama | first1 = Y | year = 2015 | title = Scale invariance vs conformal invariance | url = | journal = Physics Reports | volume = 569 | issue = | pages = 1–93 | doi=10.1016/j.physrep.2014.12.003}}</ref> For this reason, the analog of the ''C''-theorem in four dimensions is called the '''''A''-theorem'''.
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