ANNALS OF PHYSICS 200, 206-215 (1990) Anomalies from Nonfree Action of the Gauge Group A. HEIL, A. KERSCH, N. A. PAPADOPOULOS,* B. REIFENHAUSER, + AND F. SCHECK~, * Institut ftir Physik, Johannes Gutenberg-Universitit, Staudinger Weg 7, Postfach 3980, D-6500 Mainz, Federal Republic of Germany Received May 15, 1989 The question whether new anomalies appear, connected with the finite dimensional part of the gauge group isomorphic to the structure group of the theory, is investigated in a systematical way. The stability groups from the stratification of the gauge group on the space of connections lead to anomalies. The detection of these anomalies within the equivariant approach pursued here is extremely simple. For a large class of theories it is shown that no new anomalies appear. % 1990 Academic Press, Inc. 1 Quantized local gauge theories coupled to chiral fermions usually exhibit anomalies [ 11, i.e., deviations from the classical broken symmetry of the theory. As is well known anomalies are controlled by the quantum corrections of lowest non- vanishing order, due to Bardeen’s nonrenormalization theorem [ 11. This fact and the observation that anomalies appear only when chiral fermions are introduced into the theory, is at the root of their topological interpretation (see, e.g., [2]). Thus, anomalies have both local, algebraic and global, geometric aspects. The algebraic approach is instrumental in doing actual computations in the framework of local perturbation theory [2, 31 while the geometric analysis is essential in pinpointing the topological origin of anomalies. In the latter approach one is led to study the action of the (infinite dimensional) gauge group ‘9 ,on the space of connections d and to follow the reduction of the effective action to the residual (physical) space of gauge inequivalent connections (potentials). The effective action functional (obtained after integration over the fermion fields) is a section in a complex line bundle over the space of inequivalent connections, the determinant bundle, whose study was initiated by the seminal work of Atiyah and Singer [4, 51. * Supported in part by the PROCOPE program of the Deutscher Akademischer Austauschdienst (DAAD). + Supported by DFG. t Also at U.S.T.L. Montpelher and C.P.T. Marseille-Luminy, France. 206 CQO3-4916190 $7.50 Copyright 0 1990 by Academic Press. Inc. All rights ol reproduction in any form reserved.