Boundary conditions and the corresponding states of quantum field theory depend on how the horizons are taken into account. There is ambiguity as to which method is appropriate because different ways of incorporating the horizons lead to different results. We propose that a natural way of including the horizons is to first consider the maximal Kruskal extension and then define the quantum field theory on the Euclidean section. Boundary conditions emerge naturally as consistency conditions of the Kruskal extension. We carry out the proposal for the explicit case of the Schwarzschild-de Sitter manifold with two horizons. The required periodicity is the interesting condition that it is the lowest common multiple of 2 pi divided by the surface gravity of both horizons. The example also highlights some of the difficulties of the off-shell approach with conical singularities in the multi-horizon scenario; and serves to illustrate the much richer interplay that can occur between horizons, quantum field theory and topology when the cosmological constant is not neglected in black hole processes.