In bosonic string theory, the attempt is to compute the possible energy levels of a string, in particular, the lowest energy level. Speaking informally, each harmonic of the string can be viewed as a collection of ‘D’ − 2 independent quantum harmonic oscillators, one for each transverse direction, where D is the dimension of spacetime. If the fundamental oscillation frequency is ω, then the energy in an oscillator contributing to the n-th harmonic is nħω/2. So using the divergent series, the sum over all harmonics is −ħω(D − 2)/24. Ultimately it is this fact, combined with the Goddard–Thorn theorem, which leads to bosonic string theory failing to be consistent in dimensions other than 26.
is the = −12 a typo or a joke?
Typo, thanks for pointing it out. Also, see here for the physics reference: https://en.m.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_⋯
Haha what the fuck
It’s astonishing, but yes, that is the reason why that form of string theory takes place in a 26 dimensional space-time.
wait till you see E8*E8 heterotic string theory,
https://en.wikipedia.org/wiki/Heterotic_string_theory
This might be a better description: link