N=4超杨-米尔斯理论中的表面缺陷：精确结果与全息自举法
Surface defects in $\mathcal{N}=4$ Super Yang-Mills: exact results and holographic bootstrap
浏览论文内容
中文总结 AI 辅助
该研究针对N=4超杨-米尔斯理论的半BPS表面缺陷，求解超共形沃德恒等式构造超共形块，通过手征代数映射确定关联函数，提取缺陷共形场论数据并以全息自举法重现强耦合结果。
中文摘要 AI 辅助
我们研究存在半BPS表面缺陷时，N=4超杨-米尔斯理论中手征初级算符的两点关联函数。这类缺陷仅保留横向转动与整体U(1) R-对称性的对角组合，因此关联函数依赖一个额外的交叉比，并分裂为具有确定角荷的扇区。我们求解超共形沃德恒等式，构造所有扇区（包括无横向转动缺陷对应物的带电扇区）的体与缺陷超共形块。该解包含一个全纯扇区，我们通过将其映射到手征代数关联函数的方式非微扰地确定它。我们将此映射扩展到破坏横向转动的缺陷，这需要重新定义二维流代数的模式，并利用它确定带电扇区。随后，我们利用缺陷色散关系，在大N与强耦合下重构出标度维度为2的手征初级算符的完整关联函数的领头阶结果。在带电扇区中，长多重态不存在，该结果推测在N与耦合常数两方面均精确；我们在弱耦合下展开该结果，发现其与已知结果完全吻合。从这些关联函数中，我们提取出无穷多组新的缺陷共形场论数据。最后，我们通过在转动不变轨迹上进行独立的威滕图自举，重现了强耦合下的结果。
英文摘要
We study two-point functions of chiral primary operators in $\mathcal{N}=4$ Super Yang-Mills in the presence of a half-BPS surface defect. Such a defect preserves only the diagonal combination of transverse rotations and of a global U(1) R-symmetry, so that the correlator depends on one additional cross-ratio and splits into sectors of definite angular charge. We solve the superconformal Ward identities and construct the bulk and defect superconformal blocks in all sectors, including the charged ones, which have no analogue for defects preserving transverse rotations. The solution contains a holomorphic sector, which we fix non-perturbatively by mapping it to a chiral algebra correlator. We extend this map to defects breaking transverse rotations, where it requires a redefinition of the modes of the two-dimensional current algebra, and use it to fix the charged sectors as well. We then use the defect dispersion relation to reconstruct the full correlator of the dimension-two chiral primary at leading order at large N and strong coupling. In the charged sectors long multiplets are absent and the answer is conjecturally exact in both N and the coupling; expanding it at weak coupling, we find perfect agreement with known results. From these correlators we extract infinitely many new pieces of defect CFT data. Finally, we reproduce the strong-coupling answer by an independent Witten diagram bootstrap on the rotation-invariant locus.
发表机构
- École Polytechnique（巴黎综合理工学院）
机构由 AI 辅助整理，请以论文原文为准。
