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

Describes the general theory of Moonshine and its underlying concepts for graduate students and researchers; now reissued as Open Access.

Terry Gannon (Author)

9781009401555, Cambridge University Press

Paperback / softback, published 27 July 2023

492 pages
25.5 x 17.5 x 2.8 cm, 0.909 kg

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.

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: Statistical physics [PHS]