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基本説明
Presents a broad survey of many of the noteworthy developments that have taken place in string theory, geometry, and duality since the mid 1990s.
Full Description
This book presents contributions of participants of a workshop held at the Centre de Recherches Mathematiques (CRM), University of Montreal. It can be viewed as a sequel to ""Mirror Symmetry I"" (1998), ""Mirror Symmetry II"" (1996), and ""Mirror Symmetry III"" (1999), copublished by the AMS and International Press. The volume presents a broad survey of many of the noteworthy developments that have taken place in string theory, geometry, and duality since the mid 1990s.Some of the topics emphasized include the following: integrable models and supersymmetric gauge theories; theory of M- and D-branes and noncommutative geometry; duality between strings and gauge theories; and, elliptic genera and automorphic forms. Several introductory articles present an overview of the geometric and physical aspects of mirror symmetry and of corresponding developments in symplectic geometry. The book provides an efficient way for a very broad audience of mathematicians and physicists to explore the frontiers of research into this rapidly expanding area.
Contents
Calabi-Yau Manifolds, Mirror Symmetry, and Symplectic Geometry: A survey of mirror principle by B. H. Lian, K. Liu, and S.-T. Yau Mirror symmetry: aspects of the first 10 years by B. R. Greene Lagrangian torus fibrations of Calabi-Yau hypersurfaces in toric varieties and SYZ mirror symmetry conjecture by W.-D. Ruan Moduli space of stable maps by G. Liu Cohomological properties of ruled symplectic structures by F. Lalonde and D. McDuff Supersymmetric gauge theories and integrable models: Spectral Lax pairs and Calogero-Moser systems by J. C. Hurtubise M-theory tested by ${\mathcal {N}}=2$ Seiberg-Witten theory by I. P. Ennes, C. Lozano, S. G. Naculich, H. Rhedin, and H. J. Schnitzer Seiberg-Witten curves for elliptic models by I. P. Ennes, C. Lozano, S. G. Naculich, and H. J. Schnitzer The periodic and open Toda lattice by I. Krichever and K. L. Vaninsky Exact integration methods for supersymmetric Yang-Mills theory by J.-L. Gervais M-theory, D-branes, and non-commutative geometry: Nonabelian D-branes and noncommutative geometry by R. C. Meyers Evidence for winding states in noncommutative quantum field theory by P. Pouliot The discrete bound state spectrum of the rotating D0-brane system, and its decay by emission of Ramond-Ramond field radiation by K. G. Savvidy On the correspondence between D-branes and stationary supergravity solutions of type II Calabi-Yau compactifications by F. Denef Phase-transitions and tensor dynamics in $M$-theory by M. Faux, D. Lust, and B. A. Ovrut Duality, Eisenstein series and exact thresholds by N. A. Obers and B. Pioline Strings, gauge theories, and AdS/CFT correspondence: Connectedness of the boundary in the AdS/CFT correspondence by E. Witten and S.-T. Yau A note on the topology of the boundary in the AdS/CFT correspondence by S.-T. Yau Holographic duals of 4D field theories by M. Porrati and A. Starinets Black hole thermodynamics from calculations in strongly-coupled gauge theory by D. Kabat, G. Lifschytz, and D. A. Lowe Correlation functions for orbifolds of the type $M^N/S^N$ by O. Lunin and S. D. Mathur Elliptic genera and automorphic forms: Elliptic genera of singular varieties, orbifold elliptic genus and chiral de Rham complex by L. A. Borisov and A. Libgober On family rigidity theorems for Spin$^{c}$ manifolds by K. Liu and X. Ma Aample divisors, automorphic forms and Shafarevich's conjecture by J. Jorgenson and A. Todorov.
