On the stress tensor light-ray operator algebra

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