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

TL;DR

This paper introduces a gravity-dual framework for time-dependent high-energy collisions in $\mathcal{N}=4$ SYM by modeling collision debris as heavy-quark–ended strings in $AdS_5$ and proposing a two-vacuum Einstein construction separated by a matter membrane. It systematically analyzes the dynamics of falling objects—massless and massive particles, open strings, and membranes—in $AdS_5$, uncovering a universal late-time behavior $z(\tau)\sim \tau$ and deriving scaling and non-scaling string solutions, including a rectangular non-scaling regime at large rapidity. The work connects to the Janik–Peschanski stretching black-hole solution, showing how a horizon forms and evolves with time (e.g., $z_h\sim \tau^{1/3}$) and arguing that all debris approach the horizon in a universal fashion with subleading boundary stress-energy contributions of order $\mathcal{O}(1/\tau^2)$. The authors advocate a tractable two-vacuum plus membrane approximation to capture the essential gravity dynamics and lay the groundwork for computing holographic boundary observables (the stress tensor) in the sequel, thereby linking bulk dynamics to boundary hydrodynamic-like behavior. The framework aims to illuminate how equilibration and entropy production emerge in strongly coupled gauge theories from gravitational collapse in 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.

Figures (10)

• Figure 1: Schematic view of the collision setting. The classical heavy charges move along directions $x_\pm$ and collide at the origin. String snapping leads to longitudinally stretched strings (wide black line) which are also extended into the 5-th coordinate $r$ toward the AdS center at $r=0$. The heavy charges move on the plane $r=\infty$
• Figure 2: (a=upper) Two snapshot of the membrane shapes, at different time moments. See text for explanation of the coordinates. (b=lower)Schematic view of the four periods in gravity dual solution in which falling objects are (1) accelerated into the 5-th dimension $r$ till they reach a relativistic velocity $v\approx 1$, then (2) continue their relativistic fall till (3) breaking near the retreating horizon.
• Figure 3: Rapidity of the collision $Y=arctanh(v)$ vs $f_0^2$. The maximum gives a critical rapidity $Y_c$. For $Y<Y_c$, two $f_0^2$ are possible, corresponding two string configurations. For $Y=Y_c$ ,only one $f_0^2$ is possible. The region $Y>Y_c$ cannot be reached
• Figure 4: the potential V as a function of v for different branches of solution. circles for large-$f_0^2$ branch, crosses for small-$f_0^2$ branch V is plotted in unit of $\sqrt{g^2\,N}/L$ The potential from the large $f_0^2$ branch is lower than that from small $f_0^2$ branch
• Figure 5: The evolution of eigenvalue $\lambda$ from Y=0.48 to 0.18 in the complex plane