论文标题
软颗粒和无限维数几何形状
Soft Particles and Infinite-Dimensional Geometry
论文作者
论文摘要
在Sigma模型中，模量标量的软插入涉及Vacua的有限维模量空间的$ S $ -MATRIX元素和反对称双柔性定理计算真空歧管的曲率。我们在渐近平坦的空间中探讨了这些陈述的类似物，其中相关的模量空间是无限的。这些模型具有空间无穷大的（琐碎）平坦连接参数化的真空空间，以及对这些无限二维歧管的光子，胶子和重力的软插入。我们认为，$ d+2 $ bumb dimensions中的反对称双柔软的gluon定理计算无限维空间映射$（s^d，g）/g $上的连接的曲率。阿贝尔仪理论和重力中的类似指标是平坦的，如这些模型中的反对称双斜率定理的消失所表明的那样。换句话说，Feynman图计算不仅了解Yang-Mills理论的真空歧管，还可以用于计算其曲率。结果对平面全息图具有有趣的含义。
In the sigma model, soft insertions of moduli scalars enact parallel transport of $S$-matrix elements about the finite-dimensional moduli space of vacua, and the antisymmetric double-soft theorem calculates the curvature of the vacuum manifold. We explore the analogs of these statements in gauge theory and gravity in asymptotically flat spacetimes, where the relevant moduli spaces are infinite-dimensional. These models have spaces of vacua parameterized by (trivial) flat connections at spatial infinity, and soft insertions of photons, gluons, and gravitons parallel transport $S$-matrix elements about these infinite-dimensional manifolds. We argue that the antisymmetric double-soft gluon theorem in $d+2$ bulk dimensions computes the curvature of a connection on the infinite-dimensional space Map$(S^d,G)/G$. The analogous metrics in abelian gauge theory and gravity are flat, as indicated by the vanishing of the antisymmetric double-soft theorems in those models. In other words, Feynman diagram calculations not only know about the vacuum manifold of Yang-Mills theory, they can also be used to compute its curvature. The results have interesting implications for flat holography.
