moonshine theory
E656667
branch of mathematics
research area in group theory
research area in mathematical physics
research area in number theory
Moonshine theory is a branch of mathematics that uncovers deep and unexpected connections between finite simple groups (notably the Monster group), modular functions, and structures in conformal field theory and string theory.
Statements (53)
| Predicate | Object |
|---|---|
| instanceOf |
branch of mathematics
ⓘ
research area in group theory ⓘ research area in mathematical physics ⓘ research area in number theory ⓘ |
| connectedTo |
string theory compactifications
ⓘ
symmetries of K3 sigma models ⓘ two-dimensional conformal field theory ⓘ |
| developedBy |
Arne Meurman
NERFINISHED
ⓘ
Igor Frenkel NERFINISHED ⓘ James Lepowsky NERFINISHED ⓘ Jeffrey A. Harvey NERFINISHED ⓘ John F. R. Duncan NERFINISHED ⓘ John H. Conway NERFINISHED ⓘ Miranda Cheng NERFINISHED ⓘ Richard Borcherds NERFINISHED ⓘ Simon P. Norton NERFINISHED ⓘ Terry Gannon NERFINISHED ⓘ |
| field |
conformal field theory
ⓘ
group theory ⓘ modular forms ⓘ number theory ⓘ representation theory ⓘ string theory ⓘ |
| focusesOn |
Monster group
NERFINISHED
ⓘ
automorphic forms ⓘ conformal field theories ⓘ connections between finite simple groups and modular functions ⓘ modular functions ⓘ vertex operator algebras ⓘ |
| keyResult |
Borcherds proof of the monstrous moonshine conjectures
ⓘ
construction of the Monster vertex operator algebra ⓘ discovery of umbral moonshine relating Niemeier lattices and mock modular forms ⓘ realization of Monster group as automorphism group of a vertex operator algebra ⓘ |
| notableObject |
McKay–Thompson series
NERFINISHED
ⓘ
Monster group NERFINISHED ⓘ modular j-invariant NERFINISHED ⓘ |
| originatedFrom |
observations by John McKay
ⓘ
observations by John Thompson ⓘ |
| relates |
K3 surfaces
NERFINISHED
ⓘ
McKay–Thompson series NERFINISHED ⓘ Monster group NERFINISHED ⓘ Niemeier lattices NERFINISHED ⓘ modular j-function ⓘ sporadic simple groups NERFINISHED ⓘ vertex operator algebras ⓘ |
| subfield |
Mathieu moonshine
NERFINISHED
ⓘ
monstrous moonshine ⓘ umbral moonshine NERFINISHED ⓘ |
| usesConcept |
automorphic products
ⓘ
conformal field theories ⓘ mock modular forms ⓘ modular functions ⓘ vertex operator algebras ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.