论文标题
$ o（n）$模型，$ ϕ^6 $潜在的$ {\ mathbb r}^2 \ times {\ mathbb r}^+$ $
The $O(N)$ model with $ϕ^6$ potential in ${\mathbb R}^2 \times {\mathbb R}^+$
论文作者
论文摘要
我们研究了$ o（n）$ n $限制的标量场理论，在平面边界的存在下，在三个维度上具有经典边缘$ ϕ^6 $相互作用。该理论在$ n $上具有大概的共形不变性。我们发现该理论的不同阶段，与标量场的不同边界条件相对应。计算一个循环有效电位，我们检查了这些不同阶段的稳定性。电势还允许我们确定应力张量轨迹中的边界异常系数。我们进一步计算了DIRICHLET情况的电流和应力调整两个点函数，并将它们分解为边界和块状结构块。应力张量两个点功能的边界极限使我们能够计算另一个边界异常系数。两个异常系数都取决于大约边缘$ ϕ^6 $耦合。
We study the large $N$ limit of $O(N)$ scalar field theory with classically marginal $ϕ^6$ 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 $ϕ^6$ coupling.
