Local conformal symmetry and its fate at quantum level

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The purpose of this article is to present a short review of local conformal symmetry in curved 4d space-time. Furthermore we discuss the conformal anomaly and anomaly-induced effective actions. Despite the conformal symmetry is always broken at quantum level, it may be a basis of useful and interesting approximations for investigating quantum corrections.
18 pages, LaTeX. Talk presented at the Fifth International Conference on Mathematical Methods in Physics, 24 - 28, April 2006, Rio de Janeiro, Brazil. To be published by PoS/JHEP

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