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

A bstract 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 $$ \mathcal{C} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> -theorem for localized RG flows along the sub-defect and show that the $$ \mathcal{C} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> -theorem holds in our model by perturbative calculations.