Toward the AdS/CFT gravity dual for high energy collisions. I. Falling into the AdS space

Abstract

In the context of the AdS/CFT correspondence we discuss the gravity dual of a high energy collision in a strongly coupled $\mathcal{N}=4$ SYM gauge theory. We suggest a setting in which two colliding objects are made of nondynamical heavy quarks and antiquarks, which allows one to treat the process in classical string approximation. Collision ``debris'' consist of closed as well as open strings. If the latter have ends on two outgoing charges, they are being ``stretched'' along the collision axes. We discuss motion in AdS of some simple objects first---massless and massive particles---and then focus on open strings. We study the latter in considerable detail, concluding that they rapidly become ``rectangular'' in proper time-spatial rapidity $\ensuremath{\tau}\ensuremath{-}y$ coordinates with well separated fragmentation part and a near-free-falling rapidity-independent central part. Assuming that in the collisions of ``walls'' of charges multiple stretching strings are created, we also consider the motion of a 3D stretching membrane. We then argue that a complete solution can be approximated by two different vacuum solutions of Einstein equations, with matter membrane separating them. We identify one of these solutions with a Janik-Peschanski stretching black hole solution, and show that all objects approach its (retreating) horizon in a universal manner.