AI 中文总结
研究欧几里得AdS$_d$空间（$d < 4$）中与费米子或标量耦合的共形QED，用$\epsilon$展开研究相关BCFTs，计算相互作用不动点处正则化AdS自由能及边界共形数据，发现狄利克雷边界条件在$d = 3$可能无法定义稳定BCFT。
AI 中文摘要
我们研究了在欧几里得反德西特（AdS$_d$）空间中，$d < 4$时，与$N_f$个无质量费米子或$N_s$个共形耦合标量耦合的共形量子电动力学（QED）。利用围绕$d = 4$的$\epsilon$展开，我们研究了通过对规范场施加狄利克雷或诺伊曼边界条件定义的相关边界共形场论（BCFTs）。我们计算了相互作用不动点处的正则化AdS自由能，直至次领先阶，并提取了一圈时的一些边界共形数据，包括最轻单态标量算符的反常维度。对于狄利克雷边界条件，我们的$\epsilon$展开结果外推表明，这些标量算符之一在$d = 4$附近无关紧要，但在$3 < d < 4$范围内变为临界。这表明狄利克雷边界条件在$d = 3$中可能无法定义一个稳定的BCFT。
英文摘要
We study conformal Quantum Electrodynamics (QED) coupled to either $N_f$ massless fermions or $N_s$ conformally coupled scalars in Euclidean Anti-de Sitter (AdS$_d$) space for $d < 4$. Using the $ε$-expansion around $d=4$, we investigate the associated Boundary Conformal Field Theories (BCFTs) defined by imposing either Dirichlet or Neumann boundary conditions on the gauge field. We compute the regularized AdS free energy at the interacting fixed point up to next-to-leading order and extract some of the boundary conformal data at one loop, including the anomalous dimensions of the lightest singlet scalar operators. For Dirichlet boundary conditions, extrapolation of our $ε$-expansion results indicate that one of these scalar operators, which is irrelevant near $d=4$, reaches marginality within the range $3 < d < 4$. This suggests that the Dirichlet boundary condition may not define a stable BCFT in $d=3$.
Comments33 pages, 5 figures
