arXiv2020
The strongly coupled dynamics of black hole formation in bulk AdS is conjectured to be dual to the thermalization of a weakly interacting CFT on the boundary for low $N$ which, for $N\to\infty$, becomes strongly coupled. We search for this thermalization effect by utilizing the D1D5 CFT to compute effective string interactions for $N=2$. This is done by turning on a marginal deformation of the theory which twists together or untwists effective strings. For a system to thermalize, the initial state, which is far from thermal, must redistribute it's energy via interactions until a thermal state is achieved. In our case, we consider excited states of the effective strings. We compute splitting amplitudes for 1) one excitation going to three excitations and 2) two excitations going to four excitations using two insertions of the deformation. Scenario 1) corresponds to a single particle moving in AdS. Scenario 2) corresponds to two particles moving and colliding in AdS. We find that the `1 to 3' amplitude has terms which oscillate with time, $t$, where $t$ is the duration of the two deformations. We find that the `2 to 4' amplitude has similar oscillatory terms as well as secular terms which grow like $t^2$. For this case the growth implies that for large $t$ the excitations in the initial state, which carry a given energy, prefer to redistribute themselves amongst lower energy modes in the final state. This is a key feature of thermalization. Albeit in a simplified setting, we therefore argue that we have identified the thermalization vertex in the D1D5 CFT, which after repeated applications, should lead to thermalization. This ultimately maps to two particles colliding and forming a black hole in AdS, which in our case, is a fuzzball.