Continuous-symmetry breaking on surface defects

Determine whether a surface defect in a three-dimensional conformal field theory can spontaneously break a continuous internal symmetry, including the associated extraordinary-log universality behavior in the three-dimensional O(N) model.

Background

The paper studies whether a one-dimensional line defect embedded in a three-dimensional critical O(N) bulk can support spontaneous discrete symmetry breaking. Its numerical evidence suggests that the relevant domain-wall operator becomes irrelevant for sufficiently large N, allowing a stable symmetry-broken line defect for N at least 3.

The outlook extends this issue to surface defects, which have higher dimensionality and can potentially support spontaneous breaking of continuous internal symmetries. The question is connected to the extraordinary-log surface universality class observed in O(N) models and is not resolved by the line-defect analysis presented in the paper.

References

A natural direction for future work is to investigate a closely related question: can a surface defect in a three-dimensional conformal field theory spontaneously break a continuous internal symmetry?

— Symmetry-breaking line defects embedded to a 3D $O(N)$ critical bulk  (2609.03289 - Yang et al., 3 Sep 2026) in Section summary and outlook

A recent study based on the bilayer fuzzy sphere $O(3)$ model suggests that the corresponding critical value satisfies N_c>3. Following a similar strategy, it may be possible to determine the critical value $N_c$ at which the extraordinary-log surface universality class terminates.

— Symmetry-breaking line defects embedded to a 3D $O(N)$ critical bulk  (2609.03289 - Yang et al., 3 Sep 2026) in Section summary and outlook