The gravitational $\mathcal{S}$-matrix defined with an infrared (IR) cutoff factorizes into hard and soft factors. The soft factor is universal and contains all the IR and collinear divergences. Here we show, in a momentum space basis, that the intricate expression for the soft factor is fully reproduced by two boundary currents, which live on the celestial sphere. The first of these is the supertranslation current, which generates spacetime supertranslations. The second is its symplectic partner, the Goldstone current for spontaneously broken supertranslations. The current algebra has an off-diagonal level structure involving the gravitational cusp anomalous dimension and the logarithm of the IR cutoff. It is further shown that the gravitational memory effect is contained as an IR safe observable within the soft $\mathcal{S}$-matrix.

中文翻译：

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重力中的软 $$ \mathcal{S} $$-矩阵

用红外 (IR) 截止定义的引力 $\mathcal{S}$ 矩阵分解为硬因子和软因子。软因子是通用的，包含所有的 IR 和共线发散。在这里，我们在动量空间基础上表明，软因子的复杂表达式完全由两个存在于天球上的边界流再现。第一个是超平移电流，它产生时空超平移。第二个是它的辛伙伴，用于自发破坏的超级翻译的戈德斯通电流。当前代数具有非对角线水平结构，包括引力尖点异常维度和 IR 截止的对数。进一步表明，引力记忆效应包含在软 $\mathcal{S}$ 矩阵中作为 IR 安全可观测值。