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

by Terry Gannon

Overview

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 more than 100 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. Originally published in 2006, this title has been reissued as an Open Access publication on Cambridge Core.

Product Details

ISBN-13:	9781009401555
Publisher:	Cambridge University Press
Publication date:	07/27/2023
Series:	Cambridge Monographs on Mathematical Physics
Pages:	492
Product dimensions:	6.89(w) x 10.04(h) x 1.10(d)

About the Author

Terry Gannon is Professor of Mathematics at the University of Alberta, Edmonton. He is currently also Research Fellow of Alexander von Humboldt Foundation, EPSRC.

Table of Contents

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.

Editorial Reviews

"An excellent introduction to this area for anyone who is looking for an informal survey... written in a lively and readable style."
R.E. Boucherds, University of California at Berkeley for the Bulletin of the AMS

"It is written in a breezy, informal style which eschews the familiar Lemma-Theorem-Remark style in favor of a more relaxed and continuous narrative which allows a wide range of material to be included. Gannon has written an attractive and fun introduction to what is an attractive and fun area of research."
Geoffrey Mason, Mathematical Reviews


"Gannon wants to explain to us "what is really going on." His book is like a conversation at the blackboard, with ideas being explained in informal terms, proofs being sketched, and unknowns being explored. Given the complexity and breadth of this material, this is exactly the right approach. The result is informal, inviting, and fascinating."
Fernando Q. Gouvea, MAA Reviews

From the Publisher