Eric D'Hoker, Justin Kaidi

Modular Forms and String Theory

• Gebundenes Buch

Produktbeschreibung

"A practical introduction to the mathematical theory of modular forms and its physical applications to string theory, suitable for undergraduate and graduate students, and researchers who wish to navigate the intersection of cutting-edge physics and mathematics. This text offers essential insights, examples, and exercises with detailed solutions"--

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 500
• Erscheinungstermin: 13. November 2024
• Englisch
• Abmessung: 250mm x 175mm x 31mm
• Gewicht: 1034g
• ISBN-13: 9781009457538
• ISBN-10: 1009457535
• Artikelnr.: 71855840

Autorenporträt

Eric D'Hoker obtained his PhD in physics from Princeton University and is currently Distinguished Professor of Theoretical and Mathematical Physics at the University of California, Los Angeles (UCLA) and a fellow of the American Physical Society. He was previously a Simons fellow, a Dyson Distinguished Visiting Professor at Princeton's Institute for Advanced Study, and has served as President of the Aspen Center for Physics.

Inhaltsangabe

1. Introduction
Part I. Modular Forms and their Variants: 2. Elliptic functions
3. Modular forms for SL(2,Z)
4. Variants of modular forms
5. Quantum fields on a torus
6. Congruence subgroups and modular curves
7. Modular forms for congruence subgroups
8. Modular derivatives and vector-valued modular forms
9. Modular graph functions and forms
Part II. Extensions and Applications: 10. Hecke operators
11. Singular moduli and complex multiplication
12. String amplitudes
13. Toroidal compactification
14. S-duality of type IIB superstrings
15. Dualities in N = 2 super Yang-Mills theories
16. Basic Galois theory
Part III. Appendix: Appendix A Some arithmetic
Appendix B Riemann surfaces
Appendix C Line bundles on Riemann surfaces
Appendix D Riemann ¿-functions and meromorphic forms
Appendix E Solutions to exercises.