Counting states in heterotic SO(32) string theory | A First Course in String Theory

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(a) Consider the left NS’ sector. Write the precise mass-squared formula with normal-ordered oscillators and the appropriate normal-ordering constant.

The GSO projection here keeps the states with ; this defines the left NS’+ sector.

Write explicitly and count the states we keep for the three lowest mass levels, indicating the corresponding values of . [This is a long list.]

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p.314 “Let us declare that number to be minus one, thus making the ground states fermionic:”

Equation (14.39):

Equation (14.40):

p.315 “So all the states with integer have ; they are fermionic states.”

**However, in this problem:**

“The left NS’ sector is built with oscillators and acting on the vacuum , declared to have :”

So all the states with integer have .

— This answer is my guess. —

If we define in the way similar to equation (14.37), we have

Let , the number of ways to put n indistinguishable balls into k boxes.

— This answer is my guess. —

— Me@2018-10-14 03:25:08 PM

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2018.10.16 Tuesday (c) All rights reserved by ACHK