Note on surface defects in multiscalar critical models

This paper studies generic surface defects for multiscalar critical models using a perturbative $\epsilon$ expansion in $4-\epsilon$ dimensions. The beta functions of the defect couplings for a generic multiscalar bulk with quartic interactions are computed at first non-trivial order in $\epsilon$. Specific bulks of interest are then considered: $O(N)$, hypercubic, hypertetrahdral, and biconical $O(m)\times O(n)$. In each case, we compute fixed points for the defect couplings and determine the remaining bulk symmetry. Expanding beyond the $O(N)$ model, we find a greater variety of patterns of symmetry breaking.