Toward the AdS/CFT gravity dual for High Energy Collisions: I.Falling into the AdS

Abstract

In the context of the AdS/CFT correspondence we discuss the gravity dual of a high energy collision in a strongly coupled ${\cal N}=4$ SYM gauge theory. We suggest a setting in which two colliding objects are made of non-dynamical heavy quarks and antiquarks, which allows 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, and thus 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 a considerable detail, concluding that they rapidly become ``rectangular'' in proper time -spatial rapidity $τ-y$ 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 eqns, with matter membrane separating them. We identify one of this solution with Janik-Peschanski stretching black hole solution, and show that all objects approach its (retreating) horizon in an universal manner.

v2 was redone, with new material and different introduction. It now includes introduction to the second paper of the series as well, in which we calculate "holograms" of falling objects, namely their stress tensor on the boundary