Moonshine beyond the Monster
The Bridge Connecting Algebra, Modular Forms and Physics

A monograph on Moonshine, a mathematical physics topic, for graduate students and researchers.

Terry Gannon (Author)

9780521141888, Cambridge University Press

Paperback, published 22 April 2010

492 pages
24.4 x 17 x 2.5 cm, 0.78 kg

Review of the hardback: 'I personally feel that one-volume introductions to subjects of major mathematical interest and importance are invaluable, as collecting information from a variety of scattered sources and arranging it in an accessible way is a great service to those new to the field. This book does this very successfully and is a helpful contribution to the literature.' Mathematics Today

This book was originally published in 2006. Moonshine forms a way of explaining the mysterious connection between the monster finite group and modular functions from classical number theory. The theory has evolved to describe the relationship between finite groups, modular forms and vertex operator algebras. Moonshine Beyond the Monster describes the general theory of Moonshine and its underlying concepts, emphasising the interconnections between mathematics and mathematical physics. Written in a clear and pedagogical style, this book is ideal for graduate students and researchers working in areas such as conformal field theory, string theory, algebra, number theory, geometry and functional analysis. Containing over a hundred exercises, it is also a suitable textbook for graduate courses on Moonshine and as supplementary reading for courses on conformal field theory and string theory.

Acknowledgements
Introduction: glimpses of the theory beneath Monstrous moonshine
1. Classical algebra
2. Modular stuff
3. Gold and brass: affine algebras and generalisations
4. Conformal field theory: The physics of Moonshine
5. Vertex operator algebras
6. Modular group representations throughout the realm
7. Monstrous Moonshine
Epilogue
Notation
References
Index.

Subject Areas: Physics [PH], Number theory [PBH], Algebra [PBF]