Boundaries and interfaces with localized cubic interactions in the O(N) model

Sabine Harribey, Igor R. Klebanov, Zimo Sun

Research output: Contribution to journalArticlepeer-review


We explore a new approach to boundaries and interfaces in the O(N) model where we add certain localized cubic interactions. These operators are nearly marginal when the bulk dimension is 4 − ϵ, and they explicitly break the O(N) symmetry of the bulk theory down to O(N − 1). We show that the one-loop beta functions of the cubic couplings are affected by the quartic bulk interactions. For the interfaces, we find real fixed points up to the critical value N crit ≈ 7, while for N > 4 there are IR stable fixed points with purely imaginary values of the cubic couplings. For the boundaries, there are real fixed points for all N, but we don’t find any purely imaginary fixed points. We also consider the theories of M pairs of symplectic fermions and one real scalar, which have quartic OSp(1|2M) invariant interactions in the bulk. We then add the Sp(2M) invariant localized cubic interactions. The beta functions for these theories are related to those in the O(N) model via the replacement of N by 1 − 2M. In the special case M = 1, there are boundary or interface fixed points that preserve the OSp(1|2) symmetry, as well as other fixed points that break it.

Original languageEnglish (US)
Article number17
JournalJournal of High Energy Physics
Issue number10
StatePublished - Oct 2023

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • 1/N Expansion
  • Boundary Quantum Field Theory
  • Renormalization Group
  • Scale and Conformal Symmetries


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