AI 中文总结
该研究提出基于乘积解析泛函的三维共形场论自举方法，其在单关联函数能隙最大化问题中表现更优，可提升边界、加速收敛，为相关共形理论研究提供新工具。
AI 中文摘要
我们提出了一种基于乘积解析泛函的三维共形场论自举方法。该构造将一维解析泛函与维度约化相结合，为标准导数基提供了一种高效替代方案。我们对标量和自旋-2算符的单关联函数能隙最大化问题对该方法进行了基准测试。在相当的基大小下，乘积泛函基给出了更强的边界且收敛更快，这种改进在外部维度较大时尤为显著。将外部维度设为三维伊辛自旋算符的维度，我们大幅提升了领头标量维度的单关联函数上界，也优化了通过调节单一参数可达到的临界点的Nakayama-Ohtsuki必要条件。在自旋-2问题中，我们发现Δ_φ≈4.16处存在一个新的扭点，伴随极值谱的重组；同时在两类能隙最大化问题中，我们均观测到更大外部维度下的平台结构。我们的结果使乘积解析泛函成为研究含重外部算符的共形规范理论、探测全息关联函数的平坦空间极限的有前途工具，而传统方法难以处理这两类场景。
英文摘要
We introduce a bootstrap method for three-dimensional conformal field theories based on product analytic functionals. The construction combines one-dimensional analytic functionals with dimensional reduction and provides an efficient alternative to the standard derivative basis. We benchmark the method in single correlator gap maximization problems for scalar and spin-two operators. At comparable basis size, the product functional basis gives stronger bounds and converges more rapidly, with the improvement becoming especially pronounced at large external dimension. Setting the external dimension to that of the three-dimensional Ising spin operator, we substantially sharpen the single correlator upper bound on the leading scalar dimension. We also sharpen the Nakayama-Ohtsuki necessary condition for critical points accessible by tuning a single parameter. In the spin-two problem, we find a new kink near $Δ_ϕ\simeq 4.16$, accompanied by a reorganization of the extremal spectrum. We also observe plateau structures at larger external dimension in both gap-maximization problems. Our results make product analytic functionals a promising tool for conformal gauge theories with heavy external operators and for probing the flat-space limit of holographic correlators; accessing both of these scenarios is challenging for conventional methods.
Comments12 figures, 12 tables
