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.
Highlights
In many physical applications we deal with a spacetime which is regular everywhere except on a codimension two surface around which the angular coordinate changes from 0 to 2πα with α different from one
We explore a technique recently proposed in [1] and suggest a correspondence between the N-point correlation functions on a conifold and the ðN þ 1Þ-point correlation functions on a regular manifold
We apply the correspondence to study the vacuum expectation value of a scalar operator and of the energy-momentum tensor in a conformal field theory living on a spacetime with conical singularity
Summary
In many physical applications we deal with a spacetime which is regular everywhere except on a codimension two surface around which the angular coordinate changes from 0 to 2πα with α different from one. ; ð1:1Þ which being applied to a function of α extracts a linear term in ð1 − αÞ With this definition we suggest the following correspondence: PhO1ðx1Þ...ONðxNÞiα 1⁄4 hO1ðx1Þ...ONðxNÞK0ic; ð1:2Þ where subscript “c” means connected correlator, Ok are arbitrary operators, scalar or tensor, h...iα is the correlation function computed in a spacetime with conical defect, 1550-7998=2015=91(4)=044008(11). For certain symmetric geometries, such as spherical and planar regions in Minkowski space, the modular Hamiltonian is expressible in terms of energymomentum tensor As of today, these geometries are probably the only special cases when both sides of the correspondence can be evaluated independently to verify (1.2). K0 which generates angular evolution in the transverse space to Σ This operator is related to the Rindler (or modular) Hamiltonian HR as K0 1⁄4 2πHR, and it has the following integral representation: Z. The correspondence (1.2) should be valid for the correlation functions in a thermal field theory in the Rindler spacetime
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
