Induced vacuum energy-momentum tensor in the background of a cosmic string

TL;DR

This paper investigates the vacuum energy-momentum tensor induced by a massive scalar field in the background of a cosmic string and a flux-carrying brane, analyzing its dependence on various physical parameters and space dimensions.

Contribution

It provides a comprehensive analysis of the induced vacuum energy-momentum tensor in a generalized cosmic string background, including flux and tension effects, and explores the massless case with Bernoulli polynomials.

Findings

Tensor components decrease exponentially with distance from the brane.

Dependence of tensor on flux, tension, and curvature coupling is characterized.

Massless case involves Bernoulli's polynomials of even order.

Abstract

A massive scalar field is quantized in the background of a cosmic string which is generalized to a static flux-carrying codimension-2 brane in the locally flat multidimensional space-time. We find that the finite energy-momentum tensor is induced in the vacuum. The dependence of the tensor components on the brane flux and tension, as well as on the coupling to the space-time curvature scalar, is comprehensively analyzed. The tensor components are holomorphic functions of space dimension, decreasing exponentially with the distance from the brane. The case of the massless quantized scalar field is also considered, and the relevance of Bernoulli's polynomials of even order for this case is discussed.