C-theorem: Difference between revisions

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==Four-dimensional case: ''A''-theorem==

[[John Cardy]] in 1988 considered the possibility to generalise ''C''-theorem to higher-dimensional quantum field theory. He conjectured that in four spacetime dimensions, the quantity behaving monotonically under renormalization group flows, and thus playing the role analogous to the central charge {{mvar|c}} in two dimensions, is a certain anomaly coefficient which came to be denoted as {{mvar|a}}.<ref>{{cite journal | last1 = Cardy | first1 = John | year = 1988 | title = Is there a c-theorem in four dimensions? | journal = Physics Letters B | volume = 215 | issue = 4| pages = 749–752 | doi=10.1016/0370-2693(88)90054-8|bibcode =1988PhLB..215..749C }}</ref> that in four spacetime dimensions, the quantity behaving monotonically under renormalization group flows, and thus playing the role analogous to the central charge {{mvar|c}} in two dimensions, is a certain anomaly coefficient which came to be denoted as {{mvar|a}}.

For this reason, the analog of the ''C''-theorem in four dimensions is called the '''''A''-theorem'''.