STRINGS, GAUGE FIELDS & GEOMETRY BEHIND: The Legacy of Maximilian Kreuzer

by Ludmil Katzarkov (Editor), Anton Rebhan (Editor), Johanna Knapp (Editor), Radoslav Rashkov (Editor), Emanuel Scheidegger (Editor)

Overview

This book contains exclusively invited contributions from collaborators of Maximilian Kreuzer, giving accounts of his scientific legacy and original articles from renowned theoretical physicists and mathematicians, including Victor Batyrev, Philip Candelas, Michael Douglas, Alexei Morozov, Joseph Polchinski, Peter van Nieuwenhuizen, and Peter West.Besides a collection of review and research articles from high-profile researchers in string theory and related fields of mathematics (in particular, algebraic geometry) which discuss recent progress in the exploration of string theory vacua and corresponding mathematical developments, this book contains a pedagogical account of the important work of Brandt, Dragon, and Kreuzer on classification of anomalies in gauge theories. This highly cited work, which is also quoted in the textbook of Steven Weinberg on quantum field theory, has not yet been presented in full detail except in private lecture notes by Norbert Dragon.Similarly, the software package PALP (Package for Analyzing Lattice Polytopes with applications to toric geometry), which has been incorporated in the SAGE (Software for Algebra and Geometry Experimentation) project, has not yet been documented in full detail. This book contains a user manual for a new thoroughly revised version of PALP.By including these two very useful original contributions, researchers in quantum field theory, string theory, and mathematics will find added value in a pedagogical presentation of the classification of quantum gauge field anomalies, and the accompanying comprehensive manual and tutorial for the powerful software package PALP.

Product Details

ISBN-13:	9789814412568
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	10/30/2012
Sold by:	Barnes & Noble
Format:	eBook
Pages:	568
File size:	17 MB
Note:	This product may take a few minutes to download.

Table of Contents

Foreword by the Editors vii

I Gauge Field Theory, Anomalies, and Supersymmetry 1

1 BRST symmetry and cohomology N. Dragon and F. Brandt 3

2 Aspects of supersymmetric BUST cohomology F. Brandt 87

3 Character expansion for HOMFLY polynomials I. Integrability and difference equations A. Mironov A. Morozov A. Morozov 101

4 Bicategories in field theories - an invitation T. Nikolaus C. Schweigert 119

5 The compactification of IIB supergravity on S₅ revisited P. van Nieuwenhuizen 133

II String Theory and Algebraic Geometry 159

6 Max Kreuzer's contributions to the study of Calabi-Yau manifolds P. Candelas 161

7 Calabi- Yau three-folds: Poincaré polynomials and fractals A. Ashmore Y. -H. He 173

8 Conifold degenerations of Fano 3-folds as hypersurfaces in toric varieties V. Batyrev M. Kreuzer 187

9 Nonassociativity in string theory R. Blumenhagen 213

10 Counting points and Hilbert series in string theory V. Braun 225

11 Standard models and Calabi-Yaus R. Donagi 237

12 The string landscape and low energy supersymmetry M. R. Douglas 261

13 The Cardy-Cartan modular invariant J. Fuchs C. Schweigert C. Stigner 289

14 A projection to the pure spinor space S. Guttenberg 305

15 Mathieu moonshine and symmetries of K3 sigma models S. Hohenegger 315

16 Toric Deligne-Mumford stacks and the better behaved version of the GKZ hypergeometric system R. P. Horja 329

17 Fano polytopes A. M. Kasprzyk B. Nill 349

18 Dual purpose landscaping tools: Small extra dimensions in AdS/CFT J. Polchinski E. Silverstein 365

19 Notes on the relation between strings, integrable models and gauge theories R. C. Rashkov 391

20 E₁₁, generalised space-time and IIA string theory; the R ⊗ R sector A. Rocén P. West 403

21 The Kreuzer bi-homomorphism A. N. Schellekens 413

22 Emergent spacetime and black hole probes from auto-morphic forms R. Schimmrigk 427

23 How to classify reflexive Gorenstein cones H. Skarke 443

III PALP - A Package for Analyzing Lattice Polytopes 459

24 PALP - a user manual A. P. Braun J. Knapp E. Sckeidegger H. Skarke N.-O. Walliser 461

Author Index 551