Conformal Field Theory.

Description

Conformal field theory is an elegant and powerful theory in the field of high energy physics and statistics. In fact, it can be said to be one of the greatest achievements in the development of this field. Presented in two dimensions, this book is designed for students who already have a basic knowledge of quantum mechanics, field theory and general relativity. The main idea used throughout the book is that conformal symmetry causes both classical and quantum integrability. Instead of concentrating on the numerous applications of the theory, the author puts forward a discussion of the general.  Read more... Preface Contents Chapter I Conformal Symmetry and Fields I.1 Conformal Invariance I.2 Symmetries and currents I.3 Operator product expansion I.4 Central charge and Virasoro algebra I.5 Free bosons and fermions on a plane I.6 Conformed ghost systems Chapter II Representations of the Virasoro Algebra II. 1 Fields and states II. 2 Correlation functions II. 3 Conformal bootstrap II. 4 Null states II. 5 Fusion rules II. 6 Coulomb gas picture II. 7 Ising and other statistical models II. 8 Operator algebra and bootstrap in the minimal models II. 9 Felder's (BRST) approach to minimal models. Chapter III Partition Functions and BosonizationIII. 1 Free fermions on a torus III. 2 Free bosons on a torus III. 3 Chiral bosonization III. 4 Chiral bosonization on Riemann surfaces III. 5 BRST approach to minimal models on a torus Chapter IV AKM Algebras and WZNW Theories IV. 1 AKM algebras and their representations IV. 2 Sugawara-Sommerfeld construction IV. 3 WZNW theories IV. 4 Free field AKM representations IV. 5 AKM characters, and the A-D-E classification of modular invariant partition functions Chapter V Superconformal and Super-AKM Symmetries. V.1 Superconformal algebras and their unitary representationsV. 2 Super-AKM algebra and its representations V.3 Supersymmetric WZNW theories V.4 Chiral rings and Landau-Ginzburg models Chapter VI Coset Models VI. 1 Goddard-Kent-Olive construction VI. 2 Kazama-Suzuki construction VI. 3 KS construction and LG models VI. 4 Gauged WZNW theories VI. 5 Felder's (BRST) approach to coset models VI. 6 Generalized affine-Virasoro construction Chapter VII W Algebras VII. 1 W3 algebra and its generalizations VII. 2 Free field approach VII. 3 Quantum Drinfeld-Sokolov reduction. VII.4 W coset constructionChapter VIII Conformal Field Theory and Strings VIII.1 Bosonic strings in D d"26 VIII.2 Supersymmetry and picture-changing VIII.3 Extended fermionic strings VIII.4 W gravity and W strings Chapter IX Quantum 2d Gravity, and Topological Field Theories IX.1 Quantum 2d gravity IX.2 Liouville theory IX.3 Topological field theories and strings Chapter X CFT and Matrix Models X.1 Why matrix models? X.2 One-matrix model solution X.3 Multi-matrix models X.4 Matrix models and KdV Chapter XI CFT and Integrable Models XI.1 KdV-type hierarchies and flows. XI. 2 W-flowsXI. 3 WZNW models and Toda field theories XI. 4 4d self-duality and 2d integrable models XI. 5 Self-duality and supersymmetry Chapter XII Comments XII. 1 About the Literature XII. 2 Basic facts about Lie and AKM algebras XII. 3 Basic facts about V-functions XII. 4 Basic facts about Riemann surfaces XII. 5 Basic Facts about BRST and BFV XII. 6 CFT and quantum groups Bibliography Text Abbreviations Index.