Closed string degeneracies | A First Course in String Theory
(b) State the values of and give the separate degeneracies of bosons and fermions for the first five mass levels of the type IIA closed superstrings. Would the answer have the different for type IIB?
NS+ equations of (14.38):
For , the number of states is
Since , when , .
If we take in (14.66) and change the sign inside each factor in the numerator
the _only_ effect is changing the sign of each term in the generating function whose states arise with an odd number of fermions.
is the boson contribution.
is the fermion contribution.
Turning Equation (14.67) into
is equivalent to turning all into :
Me@2015.08.29 12:49 PM: Somehow, represents “contribution from fermions”.
Me@2015.08.29 12:50 PM: If you still cannot understand, try replace all with .
It is _not_ correct. Just consider it as is not correct, since the beginning factor is not considered yet.
Instead, we should present in the following way:
— Me@2018-05-08 08:50:32 PM
2018.05.08 Tuesday (c) All rights reserved by ACHK