  We consider a Gaudin magnet (central spin model) with a time-dependent
exchange couplings. We explicitly show that the Schr\"odinger equation is
analytically solvable in terms of generalized hypergeometric functions for
particular choices of the time dependence of the coupling constants. Our method
establishes a new link between this system and the SU(2) Wess-Zumino-Witten
model, and sheds new light on the implications of integrability in
out-of-equilibrium quantum physics. As an application, a driven four-spin
system is studied in detail.
