Note on surface defects in multiscalar critical models

TL;DR

This work analyzes surface defects in generic multiscalar critical models by performing a $4- obreak\epsilon$ expansion and computing the one-loop defect beta functions for a bulk with quartic interactions. By diagonalising the defect coupling matrix $h_{ij}$, the authors classify fixed points under various bulk symmetries, including $O(N)$, hypercubic, hypertetrahedral, and $O(m) imes O(n)$, and determine the corresponding symmetry-breaking patterns. They find that, while many fixed points exist with nontrivial symmetry breaking, the only fully stable defect fixed point typically does not break the bulk symmetry; higher-loop corrections and bootstrap methods could reveal additional structure and multi-defect scenarios. The results broaden the landscape of defect CFTs in multiscalar systems and suggest observable distinctions between bulk universality classes in the presence of surface defects. The analysis provides a framework for exploring defect-induced RG flows and lays groundwork for future nonperturbative studies of surface defects in dCFTs.

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 $O(m)\times O(n)$. 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.

Figures (1)

• Figure 1: Diagrams $A_0$, $A_1$, $B_0$ that contribute to the one-point function $\langle \phi_i \phi_j(0,x)\rangle$ at lowest order. The crossed circle represents the operator $\phi_i \phi_j$ while the black vertices represent insertion of bulk and defect couplings. The surface where the defect is localised is represented by the dashed line. Black vertices on the dashed line are thus defect couplings.