  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.
