Talk:C-theorem

The article states

If such a so-called C-function exists for a given quantum field theory, it tells us that the RG flow of the theory is irreversible, since the central charge of a CFT characterizes the number of its degrees of freedom.

I am not following the logic here. Does the statement assume that every C-function must be related to the central charge? AxelBoldt (talk) 03:20, 27 February 2012 (UTC)

That's not an assumption, but a fact - $c$ equals the central charge of the theory. The details are in the Zamolodchikov paper. Logosun (talk) 11:52, 10 June 2013 (UTC)

Exceptions to a-theorem

It seems that as of 2013, 'weird' behaviours at the IR end of RG-flows are more or less excluded, as the Polchinski-Rattazzi-Luty paper (1204.5221) has gained broad acceptance. Should we modify the last remark about chaotic RG flows? Logosun (talk) 11:50, 10 June 2013 (UTC)

Please be precise: What in 2013 invalidates which precise statement in the concluding remark, and what would you propose? This is not a physics newsgroup discussion, I fear. If you found an error or gap in the statements made, proceed, but the logical possibilities mapped are there. The devil is in the "more or less", satisfaction of all assumptions, and the fine print. The weird (and, even, chaotic) behaviors are there, and illustrated in practice: Wilson's "Russian doll model" won't go away.Cuzkatzimhut (talk) 13:12, 10 June 2013 (UTC)

Sorry about the vagueness of my remark above. I agree that the statements in the paper are correct, but limited in scope. The chaotic example from the Curtright et al. paper comes from a non-unitary model, for example. If you restrict to local and unitary field theories these pathological behaviours go away. Even the limit cycles from Grinstein et al. are now widely seen to originate from ambiguities in defining RG couplings (although maybe there's not yet 100% concensus there). To me it seems a bit unfair to dedicate half of the paragraph about the a-theorem to these 'weird' scenarios -- it might mislead uninformed readers in thinking that this behaviour is generic, whereas it doesn't exist in healthy field theories. Logosun (talk) 20:48, 10 June 2013 (UTC)

I'd desist from inflicting vague "healthfulness" criteria to the proverbial uninformed reader, or parsing out "fairness"? One parenthetical sentence that starts with "still" could not possibly mislead the reader. It might force her/him to read the conditions of the theorem many times and check their understanding of it; and caution their application of it. You seem to feel that the article is strictly about unitary CFT penumbra formalism. (The Grinstein et al discussion went away on its own months ago.) If you proposed something specific, correct, and protective, it would be salutary, but the condensed matter reader who reads unqualified statements stumbling on his experience may wel roll his eyes and amble away muttering about them damned self-involved stringers---just kidding. How would you coach your notional incidental reader to not misapply the theorem? In any case, you could redress the imbalance you seem to perceive not by removing stuff, but rather by adding examples which you feel better represent what you would be applying the theorem to ... a streak of neat examples the theory would change your mind on, once you stumbled on it for the first time. The stub is too laconic, as it stands, and it could use a paragraph on applications that changed your life. "Be bold" (but positive) as the WP slogan has it. Cuzkatzimhut (talk) 00:24, 11 June 2013 (UTC)