Conformal Perturbation Theory and Counter Terms for CFT_2

In this talk I will consider conformal perturbation theory for 2D CFTs, which describes infinitessimal deformations of a CFT on a moduli space. Many explorations have focused on the spectral problem, i.e. the change in conformal dimensions of operators. In these situations one may use a hard disk cutoff and a well-known set of counter terms to regulate the integrated 3-point function; this integrated 3-point function calculates the shift to the conformal dimensions. In this talk I will present the full set of counter terms which regulate all integrated n-point functions at leading order in conformal perturbation theory when using the hard disk cutoff. This full set of counter terms prove to be necessary when considering the deformation of the structure constants, which can be calculated from integrated 4-point functions. I will conclude with a check of the methods described, using the free compact boson as test case where exact expressions are available.