An indispensable resource for readers in physics and mathematics seeking a solid grasp of the mathematical tools shaping modern theoretical physics, this book comprises a practical introduction to the mathematical theory of modular forms and their application to the physics of string theory and supersymmetric Yang-Mills theory. Suitable for adventurous undergraduates, motivated graduate students, and researchers wishing to navigate the intersection of cutting-edge research in physics and mathematics, it guides readers from the theory of elliptic functions to the fascinating mathematical world of modular forms, congruence subgroups, Hecke theory, and more. Having established a solid basis, the book proceeds to numerous applications in physics, with only minimal prior knowledge assumed. Appendices review foundational topics, making the text accessible to a broad audience, along with exercises and detailed solutions that provide opportunities for practice. After working through the book, readers will be equipped to carry out research in the field.
Sprache
Verlagsort
Illustrationen
Worked examples or Exercises
Maße
Höhe: 250 mm
Breite: 175 mm
Dicke: 31 mm
Gewicht
ISBN-13
978-1-009-45753-8 (9781009457538)
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Schweitzer Klassifikation
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. Justin Kaidi obtained his PhD in physics from UCLA. After two years as a research assistant professor at the Simons Center for Geometry and Physics at Stony Brook University, he joined the University of Washington as an assistant professor. He is currently an associate professor at the Institute for Advanced Study and Department of Physics at Kyushu University.
Autor*in
University of California, Los Angeles
Kyushu University
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.
