AI 中文总结
该研究在四维共形场论中发现应力张量构造的光算符生成$\rm w_{1+\infty}$楔形子代数，还构造了生成类似S代数的光算符，明确其单粒子函数有限，并给出相关分类、计算技术及自由标量场示例。
AI 中文摘要
在一般的相互作用四维洛伦兹共形场论中，由应力张量构造的一组通用光算符被证明生成了$\rm w_{1+\infty}$环代数的楔形子代数。该代数最近被确认为渐近平直时空渐近对称中的一部分。$\rm w_{1+\infty}$生成元在标量态（也称为单粒子事件形状）中的单粒子函数被明确证明是有限的，且与无限软引力子定理塔中的通用软因子精确相关。本文还构造了生成“S代数”（$\rm w_{1+\infty}$的规范理论类似物）的第二类通用光算符，并证明其在具有自旋一守恒流的四维共形场论中具有有限的单粒子函数。除这些结果的细节外，本文还按标度维数和洛伦兹${\rm SL}(2,\mathbb{C})$权重对应力张量和守恒流光算符进行了一般分类，介绍了一种通过庞加莱递推计算对易子的通用技术，给出了包括四维共形对称代数局域版本在内的其他光算符代数的结果，并提供了自由标量场的例子。
英文摘要
In generic interacting four-dimensional Lorentzian conformal field theories, an infinite set of universal light-ray operators constructed from the stress tensor is shown to generate the wedge subalgebra of the loop algebra of ${\rm w}_{1+\infty}$. This algebra was recently identified among the asymptotic symmetries of asymptotically flat spacetimes. The one-point functions of the ${\rm w}_{1+\infty}$ generators in scalar states (also known as one-point event shapes) are explicitly demonstrated to be finite and are precisely related to universal soft factors in the infinite tower of soft graviton theorems. A second universal class of light-ray operators that generates the ''$S$ algebra,'' the gauge-theoretic analog of ${\rm w}_{1+\infty}$, is also constructed and shown to have finite one-point functions in four-dimensional conformal field theories with a spin-one conserved current. Along with the details of these results, this paper presents a general classification of stress-tensor and conserved current light-ray operators by scaling dimension and Lorentz ${\rm SL}(2,\mathbb{C})$ weights, a general technique for computing commutators by Poincaré recursion, results for other light-ray operator algebras including a local version of the four-dimensional conformal symmetry algebra, and examples for free scalar fields.
Comments62 pages + appendices
