Modular Forms and String Theory / Eric D'Hoker and Justin Kaidi.

Format:

Book

Author/Creator:

D'Hoker, Eric, author.

Kaidi, Justin, author.

Language:

English

Subjects (All):

String models--Mathematics.

String models.

Forms, Modular.

Physical Description:

1 online resource (xv, 480 pages) : digital, PDF file(s).

Edition:

First edition.

Place of Publication:

Cambridge, England : Cambridge University Press, [2025]

Summary:

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.-- Provided by publisher

Contents:

Introduction

Elliptic functions

Modular forms for SL(2, Z)

Variants of modular forms

Quantum fields on a torus

Congruence subgroups and modular curves

Modular forms for congruence subgroups

Modular derivatives and vector-valued modular forms

Modular graph functions and forms

Hecke operators

Singular moduli and complex multiplication

String amplitudes

Toroidal compactification

S-duality of Type IIB superstrings

Dualities in N=2 super Yang-Mills theories

Basic Galois theory

Appendices

Notes:

Title from publisher's bibliographic system (viewed on 29 Nov 2024).

Description based on print version record.

ISBN:

9781009457514

1009457519

9781009457521

1009457527

OCLC:

1480128468