Conformal properties of soft operators: Use of null states
Conformal properties of soft operators: Use of null states
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软算子的共形属性：空状态的使用
DOI：
10.1103/physrevd.101.106014
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发表时间：
2019
影响因子：
5
通讯作者：
Partha Paul
中科院分区：
文献类型：
--
作者：
Shamik Banerjee;Pranjal Pandey;Partha Paul
软算符，广义地说，是在闵可夫斯基空间中的天球上产生或湮灭零能量无质量粒子的算符。洛伦兹群通过保角变换作用在天球上，软算符变换为各种维数和自旋的保角原算符。在D = 4和6维时空中，研究了以软光子和引力子为最高权向量的共形表示的性质.通常，这些表示包含空向量。我们认为，从$S $-矩阵的角度来看，无穷维渐近对称性和共形不变性要求我们设置这些零向量为零。因此，相应的软算子满足天球上的线性偏微分方程。奇怪的是，这些偏微分方程是具有标量规范不变性的欧几里德规范理论在天球上的运动方程，即规范参数是球上的标量场。这些可能与大U（1）$和无穷远处的超平移变换有关。现在，由软算子满足的PDE可以通过插入软算子转换为$S $-矩阵元素的PDE。这些方程然后可以解决适当的边界条件的天球，提供了共形不变性。的解决方案确定软$S $-矩阵元素，对于不同的螺旋度的软粒子，在一个单一的标量函数。这使得Ward恒等式的渐近对称几乎可积。积分的结果当然是温伯格的软定理，但我们不能完全完成积分。最后，我们评论了零态在渐近对称的背景下和在弦理论中与时空规范对称的关系中所起的作用之间的相似性。
Soft-operators, loosely speaking, are operators which create or annihilate zero energy massless particles on the celestial sphere in Minkowski space. The Lorentz group acts on the celestial sphere by conformal transformation and the soft-operators transform as conformal primary operators of various dimension and spin. Working in space-time dimensions $D=4$ and $6$, we study some properties of the conformal representations with the (leading) soft photon and graviton as the highest weight vectors. Typically these representations contain null-vectors. We argue, from the $S$-matrix point of view, that infinite dimensional asymptotic symmetries and conformal invariance require us to set some of these null-vectors to zero. As a result, the corresponding soft-operator satisfies linear PDE on the celestial sphere. Curiously, these PDEs are equations of motion of Euclidean gauge theories on the celestial sphere with scalar gauge-invariance, i.e, the gauge parameter is a scalar field on the sphere. These are probably related to large $U(1)$ and supertranslation transformations at infinity. Now, the PDE satisfied by the soft-operator can be converted into PDE for the $S$-matrix elements with the insertion of the soft-operator. These equations can then be solved subject to appropriate boundary conditions on the celestial sphere, provided by conformal invariance. The solutions determine the soft $S$-matrix elements, for different helicities of the soft-particle, in terms of a single scalar function. This makes the Ward-identity for the asymptotic symmetry almost integrable. The result of the integration, which we are not able to perform completely, should of course be Weinberg's soft-theorem. Finally, we comment on the similarity between the roles played by null-states in the context of asymptotic symmetry and in string theory in relation to space-time gauge symmetry.
影响因子：
3.5
作者：
Adamo T
通讯作者：
Adamo T