论文标题
在伽利略形状的引导程序上
On Galilean conformal bootstrap
论文作者
论文摘要
在这项工作中，我们为加利利形成型田间理论（GCFT）开发了保形性自举。在GCFT中，希尔伯特空间可以分解为准国家及其全球后代。与通常的保形场理论不同，GCFT中的准主要状态构成了多重组，这些状态在Galilean Boost Operator下进行了块二核。更重要的是，多重组包括否定规范的状态，表明该理论不是统一的。我们计算多重组的全局块，并根据多重组的全局块讨论四点函数的扩展。此外，我们对加利利形成对称性进行谐波分析，并获得反转公式。作为应用伽利略形成性自举的第一步，我们明确构建了广义的伽利亚自由理论（GGFT）。我们通过独立使用泰勒级数扩展和反转公式的泰勒级数扩展来读取GGFT的数据，并找到确切的一致性。由于Galilean保形代数和GCFTS的非军事性，我们讨论了Galilean保串引导程序中的一些新颖特征。
In this work, we develop conformal bootstrap for Galilean conformal field theory (GCFT). In a GCFT, the Hilbert space could be decomposed into quasiprimary states and its global descendants. Different from the usual conformal field theory, the quasi-primary states in a GCFT constitute multiplets, which are block-diagonized under the Galilean boost operator. More importantly the multiplets include the states of negative norms, indicating the theory is not unitary. We compute global blocks of the multiplets, and discuss the expansion of four-point functions in terms of the global blocks of the multiplets. Furthermore we do the harmonic analysis for the Galilean conformal symmetry and obtain an inversion formula. As the first step to apply the Galilean conformal bootstrap, we construct generalized Galilean free theory (GGFT) explicitly. We read the data of GGFT by using Taylor series expansion of four-point function and the inversion formula independently, and find exact agreement. We discuss some novel features in the Galilean conformal bootstrap, due to the non-semisimpleness of the Galilean conformal algebra and the non-unitarity of the GCFTs.
