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33 results

Page 1 of 2

  • 1 - Introduction

  • Eric D'Hoker, University of California, Los Angeles, Justin Kaidi, Kyushu University
  • Book:
    Modular Forms and String Theory
    Published online:
    28 November 2024
    Print publication:
    12 December 2024, pp 1-6

  • Summary

    The goal of this book is to exhibit the profound and myriad interrelations between the mathematics of modular forms and the physics of string theory. Our presentation is intended to be informal but mathematically precise, logically complete, and reasonably self-contained. The exposition is kept as simple as possible so as to be accessible to adventurous undergraduates, motivated graduate students, and dedicated professionals interested in the interface between theoretical physics and pure mathematics. Assuming little more than a knowledge of complex function theory, we introduce elliptic functions and elliptic curves as a lead-in to modular forms and their various deep generalizations. Following an economical introduction to string theory, its perturbative expansion, toroidal compactification, and supergravity limit are used to illustrate the power of modular invariance in physics. Dualities and their realization via modular forms in Yang–Mills theories with extended supersymmetry are studied both via the Seiberg–Witten solution and via their superconformal phase. Appendices are included to review foundational topics, and 75 exercises with detailed solutions give the reader ample opportunity for practice.

  • 13 - Gone to Texas

  • Steven Weinberg, University of Texas, Austin
  • Book:
    Steven Weinberg: A Life in Physics
    Published online:
    22 November 2024
    Print publication:
    12 December 2024, pp 173-209

  • Summary

    Weinberg collaborates with Ed Witten. He becomes the youngest member of the Saturday Club of Boston. Weinberg signs up to write The Discovery of Subatomic Particles. After their continued separation due to teaching, Weinberg grows to like Austin more and more, with its social scene that crossed from academia into the public sphere. He negotiates with the Universioty of Texas for a position in Austin as the Josey Regental Chair in Science beginning in 1982. He joins the Headliners Club in Austin. Weinberg helps found the Jerusalem Winter School in Theoretical Physics. He begins exploring physical theories in higher dimensions. He attends the Shelter Island Conference in 1983. He is elected to the Philosophical Society of Texas and joined the Town and Gown Club in Austin, but quits the latter over its male-only stance, to help form a rival, the Tuesday Club (of Austin). In mid-1980s, he becomes seriously interested in string theory.

Modular Forms and String Theory
  • Eric D'Hoker, Justin Kaidi
  • Published online:
    28 November 2024
    Print publication:
    12 December 2024
  • 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.

Quantum Geometry, Matrix Theory, and Gravity
  • Harold C. Steinacker
  • Published online:
    04 April 2024
    Print publication:
    11 April 2024
  • Building on mathematical structures familiar from quantum mechanics, this book provides an introduction to quantization in a broad context before developing a framework for quantum geometry in Matrix Theory and string theory. Taking a physics-oriented approach to quantum geometry, this framework helps explain the physics of Yang–Mills-type matrix models, leading to a quantum theory of space-time and matter. This novel framework is then applied to Matrix Theory, which is defined through distinguished maximally supersymmetric matrix models related to string theory. A mechanism for gravity is discussed in depth, which emerges as a quantum effect on quantum space-time within Matrix Theory. Using explicit examples and exercises, readers will develop a physical intuition for the mathematical concepts and mechanisms. It will benefit advanced students and researchers in theoretical and mathematical physics, and is a useful resource for physicists and mathematicians interested in the geometrical aspects of quantization in a broader context.

A Short Introduction to String Theory
  • Thomas Mohaupt
  • Published online:
    31 March 2022
    Print publication:
    07 April 2022
  • Suitable for graduate students in physics and mathematics, this book presents a concise and pedagogical introduction to string theory. It focuses on explaining the key concepts of string theory, such as bosonic strings, D-branes, supersymmetry and superstrings, and on clarifying the relationship between particles, fields and strings, without assuming an advanced background in particle theory or quantum field theory, making it widely accessible to interested readers from a range of backgrounds. Important ideas underpinning current research, such as partition functions, compactification, gauge symmetries and T-duality are analysed both from the world-sheet (conformal field theory) and the space-time (effective field theory) perspective. Ideal for either self-study or a one semester graduate course, A Short Introduction to String Theory is an essential resource for students studying string theory, containing examples and homework problems to develop understanding, with fully worked solutions available to instructors.

Page 1 of 2