Abstract
We study the various head-on collisions of two bunches of D0-branes and their real-time evolution in the BFSS matrix model in classical limit. For a various matrix size N respecting the 't Hooft scaling, we find quantitative evidence for the formation of a single bound state of D0-branes at late time, which is matrix model thermalization and dual to the formation of a larger black hole.
Highlights
Is, by solving the matrix model classical equation of motion, to study quantitatively how such a bound state is formed in the real-time evolution of the large N matrix model
We study the various head-on collisions of two bunches of D0-branes and their real-time evolution in the BFSS matrix model in classical limit
Even though classical limit is justified in the weak coupling limit, since what we conduct is not the perturbative analysis near the trivial vacuum but rather the analysis seeking the time-dependent soliton configuration, this can capture non-perturbative physics
Summary
XM (M = 1, 2, · · · , 9) are N × N Hermitian matrices and (DtXM ) is the covariant derivative given by (DtXM ) = ∂tXM − [At, XM ], where At is the U(N ) gauge field This matrix model is a gravity-decoupled theory on the N D0-branes [23]. Large N bound state of D0-branes with finite temperature T with large ’t Hooft coupling is dual to a black hole (black 0-brane) with Hawking temperature T [3]. Such a bound state is described by highly non-commutative matrices. Our analysis of solving classical equation of motion is justified in hight temperature/energy limit.
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