  In this paper, we consider the mean field optimal switching problem with a
Markov chain under viscosity solution notion. Based on the conditional
distribution of the Markov chain, the value function and corresponding dynamic
programming principle (DPP) are established. The switching problem is
characterized by an obstacle equation on the Wasserstein space, and the
existence, stability, and comparison principle are obtained in the sense of
viscosity solution. In particular, we consider a two-time-scale structure and
obtain the convergence of the limit system. As an application of our
theoretical results, an innovative example concerning the stock trading problem
in a regime switching market is solved.
