论文标题
$4-ε$尺寸的超符合边界
Superconformal Boundaries in $4-ε$ dimensions
论文作者
论文摘要
三维$ \ MATHCAL {N} = 2 $超符合理论的边界可以保留原始体积超对称性的一半。有两种可能性的特征是剩余的增压的手性。根据选择的不同，其余$ 2D $边界代数展示$ \ Mathcal {n} =（0,2）$或$ \ Mathcal {n} =（1,1）$ supersymmetry。在这项工作中，我们着重于两种超对称边界的手性场的相关功能。我们使用超空间技术研究了许多相关器，并计算了两点和三点函数的超符号块。对于$ \ mathcal {n} =（1,1）$ supersymmetry，我们的某些结果可以在时空维度上进行分析，同时保持编纂固定。这为对超对称bcfts的$ε$扩展的自举分析打开了大门。在我们的分析性超级块上，我们证明，在自由理论中，手性（和抗病毒）领域的两点函数是独一无二的。一阶校正已经描述了相互作用，最多是两个免费参数。为了检查我们的分析，我们使用Feynman图研究了具有超对称边界的Wess-Zumino模型，并在扰动和自举结果之间找到完美的一致性。
Boundaries in three-dimensional $\mathcal{N}=2$ superconformal theories may preserve one half of the original bulk supersymmetry. There are two possibilities which are characterized by the chirality of the leftover supercharges. Depending on the choice, the remaining $2d$ boundary algebra exhibits $\mathcal{N}=(0,2)$ or $\mathcal{N}=(1,1)$ supersymmetry. In this work we focus on correlation functions of chiral fields for both types of supersymmetric boundaries. We study a host of correlators using superspace techniques and calculate superconformal blocks for two- and three-point functions. For $\mathcal{N}=(1,1)$ supersymmetry, some of our results can be analytically continued in the spacetime dimension while keeping the codimension fixed. This opens the door for a bootstrap analysis of the $ε$-expansion in supersymmetric BCFTs. Armed with our analytically-continued superblocks, we prove that in the free theory limit two-point functions of chiral (and antichiral) fields are unique. The first order correction, which already describes interactions, is universal up to two free parameters. As a check of our analysis, we study the Wess-Zumino model with a supersymmetric boundary using Feynman diagrams, and find perfect agreement between the perturbative and bootstrap results.
