Planar quantum quenches: Computation of exact time-dependent correlation functions at large $N$

Abstract: We study a quantum quench of an integrable quantum field theory in the planar infinite-$N$ limit. Unlike isovector-valued $O(N)$ models, matrix-valued field theories in the infinite-$N$ limit are not solvable by the Hartre-Fock approximation, and are nontrivial interacting theories. We study quenches with initial states that are color-charge neutral, correspond to integrability-preserving boundary conditions, and that lead to nontrivial correlation functions of operators. We compute exactly at infinite $N$, the time-dependent one- and two-point correlation functions of the energy-momentum tensor and renormalized field operator after this quench using known exact form factors. This computation can be done fully analytically, due the simplicity of the initial state and the form factors in the planar limit. We also show that this type of quench preserves factorizability at all times, allows for particle transmission from the pre-quench state, while still having nontrivial interacting post-quench dynamics.