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.

中文翻译：

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在 ℝ2 × ℝ+ 中具有 ϕ6 势的 O(N ) 模型

我们研究了 O(N ) 标量场理论的大 N 极限，在存在平面边界的情况下，在三个维度上具有经典的边际 ϕ6 相互作用。该理论在大 N 处具有近似的保形不变性。我们发现理论的不同阶段对应于标量场的不同边界条件。计算单循环有效电位，我们检查这些不同阶段的稳定性。电位还允许我们确定应力张量轨迹中的边界异常系数。我们进一步计算 Dirichlet 情况的电流和应力张量两点函数，并将它们分解为边界和体共形块。应力张量两点函数的边界限制允许我们计算另一个边界异常系数。