Description:

The book is considered a systematic presentation of the modern quantum field theory of non-linear sigma-models. The contents is based on original papers. Geometrical 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-model. Supersymmetric extensions are given for most contructions, 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 sutdents and researchers in physics and mathematics.