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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.
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