Abstract

We consider d-dimensional Euclidean CFTs on a cylinder perturbed by a relevant or marginal operator. We discuss perturbation theory series for the components of the perturbed theory vacuum and show that they have a new kind of divergences  that appear when the dimension of the perturbing operator exceeds the threshold value of (d+1)/2. If left unrenormalised these divergences make  the overlap of the perturbed and unperturbed theory vacua vanish that is known in the literature as the orthogonality catastrophe. We discuss renormalisation of the vacuum vector in terms of the interface between the perturbed and unperturbed theories and possible implications for truncated Hamiltonian techniques. A number of explicit examples will be  discussed as well as some old results  which are usually linked to Haag’s theorem in infinite volume.