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On the stress tensor light-ray operator algebra
Journal of High Energy Physics ( IF 5.4 ) Pub Date : 2021-05-05 , DOI: 10.1007/jhep05(2021)033
Alexandre Belin , Diego M. Hofman , Grégoire Mathys , Matthew T. Walters

We study correlation functions involving generalized ANEC operators of the form \( \int {dx}^{-}{\left({x}^{-}\right)}^{n+2}{T}_{--}\left(\overrightarrow{x}\right) \) in four dimensions. We compute two, three, and four-point functions involving external scalar states in both free and holographic Conformal Field Theories. From this information, we extract the algebra of these light-ray operators. We find a global subalgebra spanned by n = {2, −1, 0, 1, 2} which annihilate the conformally invariant vacuum and transform among themselves under the action of the collinear conformal group that preserves the light-ray. Operators outside this range give rise to an infinite central term, in agreement with previous suggestions in the literature. In free theories, even some of the operators inside the global subalgebra fail to commute when placed at spacelike separation on the same null-plane. This lack of commutativity is not integrable, presenting an obstruction to the construction of a well defined light-ray algebra at coincident \( \overrightarrow{x} \) coordinates. For holographic CFTs the behavior worsens and operators with n2 fail to commute at spacelike separation. We reproduce this result in the bulk of AdS where we present new exact shockwave solutions dual to the insertions of these (exponentiated) operators on the boundary.

A preprint version of the article is available at ArXiv.


中文翻译:

关于应力张量的光线算子代数

我们研究相关函数,涉及形式为\(\ int {dx} ^ {-} {\ left({x} ^ {-} \ right)} ^ {n + 2} {T} _ {- } \ left(\ overrightarrow {x} \ right)\)四个维度。我们计算自由,全息共形场理论中涉及外部标量状态的两点,三点和四点函数。从这些信息中,我们提取出这些光线算子的代数。我们找到一个全球性的子代数跨区ñ = { - 2 , - 1 0 1 2}消除了保形不变的真空,并在保持光线的共线保形基团的作用下相互转化。与文献中先前的建议一致,超出此范围的运算符产生一个无限的中心术语。在自由理论中,即使将整体子代数内的某些算子放在同一个零平面上的空间状间隔中,也无法进行交换。这种可交换性的不足是不可积分的,这在重合的\(\ overrightarrow {x} \)坐标处妨碍了清晰定义的光线代数的构造。对于全息CFT,其行为恶化并且n−的算子2未能以类似空间的间隔上下班。我们在大量的AdS中重现了这一结果,在此我们提出了新的精确冲击波解决方案,这些解决方案是这些(幂)运算符在边界上的插入的双重形式。

该文章的预印本可在ArXiv上获得。
更新日期:2021-05-06
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