Correlation functions on conical defects

TL;DR

This paper introduces a new method to compute correlation functions on spacetimes with conical defects by relating them to higher-point functions in Minkowski space, verified through conformal field theory examples.

Contribution

It proposes a systematic correspondence between correlation functions on conical defects and in Minkowski space, enabling easier calculations and extending previous results.

Findings

Exact agreement with earlier results for cosmic string spacetime

Derived new correlation function computations for generic scalar and vector operators

Computed energy momentum tensor expectation values using spectral representation

Abstract

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.