Modular Forms and String Theory

Auteur

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.

Texte du rabat

"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"--

Contenu

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.