Local BRST cohomology in gauge theories

The general solution of the anomaly consistency condition (Wess-Zumino equa tion) has been found recently for Yang-Mills gauge theory. The general form of the counterterms arising in the renormalization of gauge-invariant oper ators (Kluberg-Stern and Zuber conjecture) and in gauge theories of the Yan g-Mills type with non-power counting renormalizable couplings has also been worked out in any number of space-time dimensions. This Physics Report is devoted to reviewing in a self-contained manner these results and their pro ofs. This involves computing cohomology groups of the differential introduc ed by Becchi, Rouet, Stora and Tyutin, with the sources of the BRST variati ons of the fields ("antifields") included in the problem. Applications of t his computation to other physical questions (classical deformations of the action, conservation laws) are also considered. The general algebraic techn iques developed in the Report can be applied to other gauge theories, for w hich relevant references are given. (C) 2000 Elsevier Science B.V. All righ ts reserved.