Estimating the experimental value of the electromagnetic fine structure constant α¯0=1/137.036 using the Leech lattice in conjunction with the monster group and Spher’s kissing number in 24 dimensions

Abstract

Abstract We start with various observations regarding the kissing number in the 24-dimensional Leech lattice N τ ( 24 ) = 196560 as well as the j-function coefficient b = 196884 and the minimal dimension in which the monster group can act Dm = 196883. Subsequently based on the previous results and earlier numerical experiments, we use a quibic potential to derive a quadratic equation x 2 + 128 20 x - ( N τ ( 24 ) / 10 ) = 0 where 128 = spin 7 = (2)7, 10 = D(10) and N τ ( 24 ) = 196560 are the spin representation, the super string dimension and the Leech kissing number, respectively. It is found that the only positive solution of this equation is x 1 = 137.036 = α ¯ 0 which is the accurate experimental value of inverse of the electromagnetic fine structure constant. This remarkable result is interpreted in terms of the connection between the Moonshine conjecture and string theory as well as the E-infinity relation between the kissing number in 10 dimensions K τ ( 10 ) = 336 and the degrees of freedom of Klein’s modular space dim Γ(7) = 336.