Lectures on String Theory

– 112 –
and similar for ML 2 . For the case of open string we have
( ∑
α ′ MR 2 =
n>0
α i −nα i n + ∑ r>0
)
rb i −rb i r − a .
α ′ mass 2 rep of SO(8) little (−1) F rep of little
group
group
NS − sector
− 1 2
|0〉 SO(9) −1 1
0 b i −1/2|0〉
} {{ }
8 v
SO(8) +1 8 v
+ 1 α i 2
}
−1|0〉 , b i
{{ }
−1/2b j −1/2
} {{ |0〉
}
8 v
28
SO(9) −1 36
+1
b i −1/2b j −1/2 bk −1/2|0〉
} {{ }
56 v
+1 SO(9) 84 + 44
α−1b i j −1/2
} {{ |0〉
}
1+28+35 v
, b i −3/2|0〉
} {{ }
8 v
+1
R − sector
|a〉
}{{}
+1 8 s
8 s
0 SO(8)
|ȧ〉
}{{}
8 c
−1 8 c
α−1|a〉
i ,
} {{ }
b i }
−1|ȧ〉
{{ }
+1 128
8 c +56 c 8 s +56 s
+1 SO(9)
α−1|ȧ〉
i ,
} {{ }
b i }
−1|a〉
{{ }
−1 128
8 s +56 s 8 c +56 c
Tab. 5. The lowest levels of the open fermionic string spectrum.