  We study relevant deformations of conformal field theory on a cylinder using
conformal perturbation theory, and in particular the one point function of the
deformation operator and the energy in a system after a quench. We do the one
point function calculation in both AdS and the conformal field theory and we
show that the results match. Our calculations are done with arbitrary spacetime
dimension, as well as arbitrary scaling dimension of the relevant operator. The
only singularities that appear in the end calculation can be related to
logarithmic singularities in dimensional regularization. We also study time
dependent setups in the field theory and we show how the response of the system
can be calculated in a Hamiltonian based approach. We use this procedure to
explain certain short time universal results that have been found previously.
