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Vacuum polarization induced by a cosmic string in anti-de Sitter spacetime

In this paper we investigate the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor associated with a massive scalar quantum field induced by a generalized cosmic string in D-dimensional anti-de Sitter (AdS) spacetime. In order to develop this analysis we evaluate the corresponding Wightman function. As we shall observe, this function is expressed as the sum of two terms: the first one corresponds to the Wightman function in pure AdS bulk and the second one is induced by the presence of the string. The second contribution is finite at coincidence limit and is used to provide closed expressions for the parts in the VEVs of the field squared and the energy-momentum tensor induced by the presence of the string. Because the analysis of vacuum polarizations effects in pure AdS spacetime have been developed in the literature, here we are mainly interested in the investigation of string-induced effects. We show that the curvature of the background spacetime has an essential influence on the VEVs at distances larger than the curvature radius. In particular, at large distances the decay of the string-induced VEVs is power-law for both massless and massive fields. The string-induced parts vanish on the AdS boundary and they dominate the pure AdS part for points near the AdS horizon.