# 2D CFT and the $c$-theorem

Does the $$c$$-theorem imply that in two dimensions all RG-Fixpoints are CFTs? Or does it just imply that the monotonously decreasing function $$c$$ coincides with the central charge if the fixpoint is a CFT?

• WP. Linked; and; ... May 9, 2020 at 19:58
• May 9, 2020 at 20:25
• Counter-example: the Pakrovsky-Talapov phase transition between commensurate and incommensurate phases in two dimensions is an RG fixed point but it is not conformal. For more information on this and related phase transitions, see for example the review article P. Bak, Rep. Prog. Phys., 45, 6 (1982). May 11, 2020 at 0:38