Gannon T. Moonshine beyond the Monster: The Bridge Connecting Algebra, Modular Forms and Physics

Cambridge University Press, 2006 — 492 pp. — (Cambridge Monographs on Mathematical Physics) — ISBN 9780511245145 (eBook), 9780521835312 (hardback)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, the first book of its kind, describes the general theory of Moonshine and its underlying concepts, emphasising the interconnections between modern 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.This was the first authored book on Moonshine and it will have wide appeal
A burgeoning research area, showing the connectedness of a variety of topics
Written in a clear and pedagogical style, emphasising the fundamental ideas and interesting examplesAcknowledgements
Introduction: glimpses of the theory beneath Monstrous moonshine
Classical algebra
Modular stuff
Gold and brass: affine algebras and generalisations
Conformal field theory: The physics of Moonshine
Vertex operator algebras
Modular group representations throughout the realm
Monstrous Moonshine
Epilogue
Notation