The O(N) model with ϕ 6 potential in ℝ2 × ℝ+

Christopher P. Herzog, Nozomu Kobayashi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


We study the large N limit of O(N) scalar field theory with classically marginal ϕ6 interaction in three dimensions in the presence of a planar boundary. This theory has an approximate conformal invariance at large N. We find different phases of the theory corresponding to different boundary conditions for the scalar field. Computing a one loop effective potential, we examine the stability of these different phases. The potential also allows us to determine a boundary anomaly coefficient in the trace of the stress tensor. We further compute the current and stress-tensor two point functions for the Dirichlet case and decompose them into boundary and bulk conformal blocks. The boundary limit of the stress tensor two point function allows us to compute the other boundary anomaly coefficient. Both anomaly coefficients depend on the approximately marginal ϕ6 coupling.

Original languageEnglish
Article number126
JournalJournal of High Energy Physics
Issue number9
Publication statusPublished - 1 Sept 2020


  • 1/N Expansion
  • Boundary Quantum Field Theory
  • Conformal Field Theory


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