The N: From Calabi-Yau Manifolds to Topological Field-theoriesWorld Scientific, 1995 - 468 pages This book presents, in a unifying perspective, the topics related to N=2 supersymmetry in two dimensions. Beginning with the K hler structure of D=4 supergravity Lagrangians, through the analysis of string compactifications on Calabi-Yau manifolds, one reaches the heart of the matter with the chiral ring structure of N=2 conformal field theories and its relation to topological field theory models and Landau-Ginzburg models. In addition, mirror symmetry, topological twists and Picard-Fuchs equations are discussed. |
Contents
AN INTRODUCTION TO THE SUBJECT | 1 |
SUPERGRAVITY AND KÄHLER GEOMETRY | 3 |
A BIT OF GEOMETRY AND TOPOLOGY | 25 |
1 | 65 |
COMPACTIFICATIONS ON CALABIYAU MANIFOLDS | 93 |
free supergravity | 115 |
TOPOLOGICAL FIELD THEORIES | 259 |
PICARDFUCHS EQUATIONS AND MIRROR MAPS | 363 |
| 447 | |
FAREWELL | 449 |
196 | 464 |
Common terms and phrases
action anti-ghosts B-model B-twisted Bianchi identities bosonic BRST algebra Calabi-Yau manifolds Calabi-Yau n-fold calculation Chapter Chern class chiral ring classical coefficients cohomology groups compactifications complex structure conformal field theory consider correlation functions corresponding coupling constants curvature defined definition deformations denotes derivative differential equation dimension Dolbeault cohomology Euler fermionic flat coordinates gauge theory gauge-fixing ghost number given Hence holomorphic homogeneous homology hypersurface instanton invariant Kähler 2-form Kähler class Kähler manifold Kähler potential lagrangian Landau-Ginzburg model linear Lorentz matrix metric mirror moduli space multiplet N=2 superconformal N=2 theory namely obtain operator parameters Phys Picard-Fuchs equations polynomial quantum rational curves Riemann scalar solution special geometry special Kähler spin supergravity superpotential superpotential W(X supersymmetry symmetry symplectic target manifold tensor theorem topological field theories topological Landau-Ginzburg topological sigma model topological twist transformations vanishing world-sheet Yang-Mills theory Yukawa couplings zero zero-modes