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Extension of monster moonshine to \(c = 24k\) conformal field theories. (English) Zbl 1275.81078

Summary: We present a family of conformal field theories (or candidates for CFTs) that is build on extremal partition functions. Spectra of these theories can be decomposed into the irreducible representations of the Fischer-Griess Monster sporadic group. Interesting periodicities in the coefficients of extremal partition functions are observed and interpreted as a possible extension of Monster moonshine to \(c = 24k\) holomorphic field theories.
For related results see the authors’ paper in Nucl. Phys., B 744, No. 3, 380–397 (2006; Zbl 1214.81248).

MSC:

81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
20D08 Simple groups: sporadic groups
11F22 Relationship to Lie algebras and finite simple groups
17B69 Vertex operators; vertex operator algebras and related structures
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations

Citations:

Zbl 1214.81248
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