Ketov S.V. Quantum Non-linear Sigma-Models. From Quantum Field Theory to Supersymmetry, Conformal Field Theory, Black Holes and Strings

Springer-Verlag Berlin Heidelberg 2000. — (Theoretical and Mathematical Physics). — 420 pp. — ISBN: 978-3-642-08688-5 (Print) 978-3-662-04192-5 (Online).The book is considered a systematic presentation of the modern quantum field theory of non-linear sigma-models. The content is based on original papers. Geometric properties and renormalization of a generic non-linear sigma-model are considered in detail, and illustrated by explicit multi-loop calculations in perturbation theory. Some non-perturbative results are derived for the conformally invariant non-linear sigma-models. Supersymmetric extensions are given for most constructions, with emphasis on their relation to complex geometry. Applications of non-linear sigma-models in conformal theory, gauge theory, string theory, and general relativity are given. The book addresses graduate students and researchers in physics and mathematics.