Modular Forms and String Theory
Modular Forms and String Theory
£59.99
GBPAn 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.
- Brings together a presentation of two areas of intense current research - modular forms in mathematics, and string theory and Yang-Mills theory – and exposes their numerous and far-reaching interrelations
- Introduces modular forms in a step-by-step manner using explicit theorems, proofs, examples, and exercises with detailed solutions
- Presents a gradual introduction of physical concepts and applications of modular forms accessible to readers with a minimal physics background
Product details
December 2024Hardback
9781009457538
500 pages
252 × 177 × 30 mm
1.016kg
Available
Table of Contents
- 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 Ï‘-functions and meromorphic forms
- Appendix E Solutions to exercises.
