Wilsonian renormalisation of CFT correlation functions: Field theory Lizana, J. M. Pérez-Victoria, Manuel Renormalization Group Conformal Field Theory Renormalization Regularization and Renormalons We examine the precise connection between the exact renormalisation group with local couplings and the renormalisation of correlation functions of composite operators in scale-invariant theories. A geometric description of theory space allows us to select convenient non-linear parametrisations that serve different purposes. First, we identify normal parameters in which the renormalisation group flows take their simplest form; normal correlators are defined by functional differentiation with respect to these parameters. The renormalised correlation functions are given by the continuum limit of correlators associated to a cutoff-dependent parametrisation, which can be related to the renormalisation group flows. The necessary linear and non-linear counterterms in any arbitrary parametrisation arise in a natural way from a change of coordinates. We show that, in a class of minimal subtraction schemes, the renormalised correlators are exactly equal to normal correlators evaluated at a finite cutoff. To illustrate the formalism and the main results, we compare standard diagrammatic calculations in a scalar free-field theory with the structure of the perturbative solutions to the Polchinski equation close to the Gaussian fixed point. 2018-02-15T12:58:48Z 2018-02-15T12:58:48Z 2017-06-26 info:eu-repo/semantics/article Lizana, J.M.; Pérez-Victoria, M. Wilsonian renormalisation of CFT correlation functions: Field theory. Journal of High Energy Physics, 6: 139 (2017). [http://hdl.handle.net/10481/49578] 1029-8479 http://hdl.handle.net/10481/49578 10.1007/JHEP06(2017)139 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ info:eu-repo/semantics/openAccess Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License Springer