Note on surface defects in multiscalar critical models

Abstract This paper studies generic surface defects for multiscalar critical models using a perturbative ε expansion in 4 − ϵ dimensions. The beta functions of the defect couplings for a generic multiscalar bulk with quartic interactions are computed at first non-trivial order in ε . Specific bulks of interest are then considered: O ( N ), hypercubic, hypertetrahdral, and biconical O ( m ) × 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.