Mirror Symmetry IV

Mirror Symmetry IV

by Eric D'Hoker
     
 

The volume presents a broad survey of many noteworthy developments since the publication of the previous volume, Mirror Symmetry III (AMS and International Press, 1999). Included are recent advancements in the theory of mirror manifolds and the related areas of complex and symplectic geometry emphasizing the following topics: integrable models and

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Overview

The volume presents a broad survey of many noteworthy developments since the publication of the previous volume, Mirror Symmetry III (AMS and International Press, 1999). Included are recent advancements in the theory of mirror manifolds and the related areas of complex and symplectic geometry emphasizing the following topics: integrable models and supersymmetric gauge theories; theory of M- and D-branes and noncommutative geometry; duality between strings and gauge theories; elliptic genera and automorphic forms. Several introductory articles present an overview of geometric and of 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 in this rapidly expanding area.

Product Details

ISBN-13:
9780821833353
Publisher:
American Mathematical Society
Publication date:
01/01/2003
Series:
AMS/IP Studies in Advanced Mathematics Series, #33
Pages:
381
Product dimensions:
7.20(w) x 10.20(h) x 1.00(d)

Table of Contents

Introduction
A Survey of Mirror Principle3
Mirror Symmetry: Aspects of the First 10 Years11
Lagrangian torus fibrations of Calabi-Yau hypersurfaces in toric varieties and SYZ mirror symmetry conjecture33
Moduli Space of Stable Maps57
Cohomological properties of ruled symplectic structures79
Spectral Lax pairs and Calogero-Moser systems103
M-Theory tested by N = 2 Seiberg-Witten Theory113
Seiberg-Witten curves for elliptic models127
The periodic and open Toda lattice139
Exact Integration Methods for Supersymmetric Yang-Mills Theory159
Nonabelian D-branes and Noncommutative Geometry169
Evidence for Winding States in Noncommutative Quantum Field Theory187
The Discrete Bound State Spectrum of the Rotating DO-brane System, and its Decay by Emission of Ramond-Ramond Field Radiation195
On the correspondence between D-branes and stationary supergravity solutions of type II Calabi-Yau compactifications209
Phase-Transitions and Tensor Dynamics in M-theory231
Duality, Eisenstein Series and Exact Thresholds255
Connectedness of the Boundary in the AdS/CFT Correspondence273
A note on the topology of the Boundary in the AdS/CFT Correspondence289
Holographic duals of 4D field theories291
Black Hole Thermodynamics from Calculations in Strongly-Coupled Gauge Theory299
Correlation functions for orbifolds of the type M[superscript N] / S[superscript N]311
Elliptic genera of singular varieties, orbifold elliptic genus and chiral de Rham complex325
On Family Rigidity Theorems for Spin Manifolds343
Ample Divisors, Automorphic Forms and Shafarevich's Conjecture361

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