We explore the new technique developed recently in \cite{Rosenhaus:2014woa} and suggest a correspondence between the N-point correlation functions on spacetime with conical defects and the (N+1)-point correlation functions in regular Minkowski spacetime. This correspondence suggests a new systematic way to evaluate the correlation functions on spacetimes with conical defects. We check the correspondence for the expectation value of a scalar operator and of the energy momentum tensor in a conformal field theory and obtain the exact agreement with the earlier derivations for cosmic string spacetime. We then use this correspondence and do the computations for a generic scalar operator and a conserved vector current. For generic unitary field theory we compute the expectation value of the energy momentum tensor using the known spectral representation of the 2-point correlators of stress-energy tensor in Minkowski spacetime.