Exact thermal correlators of holographic CFTs

We compute the exact retarded Green's functions in thermal $CFT$s with chemical potential and angular momenta using holography respectively. consider field equations satisfied by quasi-normal modes both charged rotating black holes $AdS$ spacetime mapped them to Heun appropriate changes of variables. The AGT correspondence allows us find connection formulae among solutions near different singularities crossing relations five-point correlators Liouville $CFT$. associated boundary conditions imposed on bulk yield