Localized RG flows on composite defects and $ \mathcal{C} $-theorem

We consider a composite defect system where a lower-dimensional defect (sub-defect) is embedded to a higher-dimensional one, and examine renormalization group (RG) flows localized on the defect. A composite defect is constructed in the (3 − ϵ)-dimensional free O(N) vector model with line and surface interactions by triggering localized RG flows to non-trivial IR fixed points. Focusing on the case where the symmetry group O(N) is broken to a subgroup O(m) × O(N − m) on the line defect, there is an O(N) symmetric fixed point for all N, while two additional O(N) symmetry breaking ones appear for N ≥ 23. We also examine a $$ \mathcal{C} $$ C -theorem for localized RG flows along the sub-defect and show that the $$ \mathcal{C} $$ C -theorem holds in our model by perturbative calculations.