Quantum Non-linear Sigma-Models: From Quantum Field Theory to Supersymmetry, Conformal Field Theory, Black Holes and Strings (Theoretical and Mathematical Physics)

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. Front Matter....Pages I-XII Introduction....Pages 1-4 Classical Structure and Renormalization....Pages 5-56 Supersymmetric NLSM....Pages 57-90 NLSM and Extended Superspace....Pages 91-164 NLSM and 2d Conformal Field Theory....Pages 165-201 NLSM and Strings....Pages 203-244 Chiral (1,0) NLSM and Heterotic Strings....Pages 245-293 LEEA in 4d, N = 2 Gauge Field Theories....Pages 295-345 Generalizations of NLSM....Pages 347-398 Back Matter....Pages 399-420 Non-Linear Sigma-Models in Two Dimensions Supersymmetric Non-Linear Sigma-Models in Two Dimensions Non-Linear Sigma-Models and Conformal Field Theory Non-Linear Sigma-Models and Strings Anomalies of Two-Dimensional Non-Linear Sigma-Models Non-Linear Sigma-Models in Four Dimensions Appendices. This Is The First Comprehensive Presentation Of The Quantum Non-linear Sigma-models. The Original Papers Consider In Detail Geometrical Properties And Renormalization Of A Generic Non-linear Sigma-model, Illustrated By Explicit Multi-loop Calculations In Perturbation Theory.