  We study co-dimension two monodromy defects in theories of conformally
coupled scalars and free Dirac fermions in arbitrary $d$ dimensions. We
characterise this family of conformal defects by computing the one-point
functions of the stress-tensor and conserved current for Abelian flavour
symmetries as well as two-point functions of the displacement operator. In the
case of $d=4$, the normalisation of these correlation functions are related to
defect Weyl anomaly coefficients, and thus provide crucial information about
the defect conformal field theory. We provide explicit checks on the values of
the defect central charges by calculating the universal part of the defect
contribution to entanglement entropy, and further, we use our results to
extract the universal part of the vacuum R\'enyi entropy. Moreover, we leverage
the non-supersymmetric free field results to compute a novel defect Weyl
anomaly coefficient in a $d=4$ theory of free $\mathcal{N}=2$ hypermultiplets.
Including singular modes in the defect operator product expansion of
fundamental fields, we identify notable relevant deformations in the singular
defect theories and show that they trigger a renormalisation group flow towards
an IR fixed point with the most regular defect OPE. We also study Gukov-Witten
defects in free $d=4$ Maxwell theory and show that their central charges
vanish.
