This book presents a modern view of anomalies in quantum field theories. It is divided into six parts. The first part is preparatory covering an introduction to fermions, a description of the classical symmetries, and a short introduction to conformal symmetry. The second part of the book is devoted to the relation between anomalies and cohomology. The third part deals with perturbative methods to compute gauge, diffeomorphism and trace anomalies. In the fourth part the same anomalies are calculated with non-perturbative heat-kernel-like methods. Part five is devoted to the family's index theorem and its application to chiral anomalies, and to the differential characters and their applications to global anomalies. Part six is devoted to special topics including a complete calculation of trace and diffeomorphism anomalies of a Dirac fermion in a MAT background in two dimensions, Wess-Zumino terms in field theories, sigma models, their local and global anomalies and their cancelation, and finally the analysis of the worldsheet, sigma model, and target space anomalies of string and superstring theories. The book is targeted to researchers and graduate students.

This volume contains the invited contributions to the NATO Advanced Research Workshop on Integrable Quantum Field Theories held at the Villa Olmo, Como, Italy, September 14-18, 1992. About 70 researchers from all over world gathered at this in- terdisciplinary workshop, which turned out to be timely and very stimulating. We are grateful to the institutions that made it possible: the NATO Scientific Affairs Divi- sion, the Istituto Nazionale di Fisica Nucleare and the Scuola Internazionale Superiore di Studi Avanzati for financial support, and the Centro A.Volta for hospitality. In the past decades integrability was mostly explored in the framework of mathe- matical physics. However, in the last few years it has become a prominent subject in many domains of theoretical physics: two dimensional statistical mechanical models, two-dimensional conformal field theories and their perturbations, matrix models of two-dimensional gravity. This trend has been confirmed by the workshop: progress has been reported in all of the above topics both from physicists and mathematicians. One can recognize three broad groups of subjects: 1) 2D lattice models and off-critical solvable models, 2) Kac-Moody algebras and their role in integrable theories, 3) matrix models of string theory and their relation with topological and integrable field theories.

This volume contains the invited contributions to the NATO Advanced Research Workshop on Integrable Quantum Field Theories held at the Villa Olmo, Como, Italy, September 14-18, 1992. About 70 researchers from all over world gathered at this in- terdisciplinary workshop, which turned out to be timely and very stimulating. We are grateful to the institutions that made it possible: the NATO Scientific Affairs Divi- sion, the Istituto Nazionale di Fisica Nucleare and the Scuola Internazionale Superiore di Studi Avanzati for financial support, and the Centro A.Volta for hospitality. In the past decades integrability was mostly explored in the framework of mathe- matical physics. However, in the last few years it has become a prominent subject in many domains of theoretical physics: two dimensional statistical mechanical models, two-dimensional conformal field theories and their perturbations, matrix models of two-dimensional gravity. This trend has been confirmed by the workshop: progress has been reported in all of the above topics both from physicists and mathematicians. One can recognize three broad groups of subjects: 1) 2D lattice models and off-critical solvable models, 2) Kac-Moody algebras and their role in integrable theories, 3) matrix models of string theory and their relation with topological and integrable field theories.