String Theory and M-Theory

are given by
4.6 Light-cone gauge quantization of the RNS string 137
|+〉R ⊗ |+〉R, (4.119)
˜ b i −1/2 |0〉NS ⊗ b j
−1/2 |0〉NS, (4.120)
˜ b i −1/2 |0〉NS ⊗ |+〉R, (4.121)
|+〉R ⊗ b i −1/2 |0〉NS. (4.122)
Since |+〉R represents an eight-component spinor, each of the four sectors
contains 8 × 8 = 64 physical states.
For the type IIA theory the left- and right-moving R-sector ground states
are chosen to have the opposite chirality. The massless states in the spectrum
are given by
|−〉R ⊗ |+〉R, (4.123)
˜ b i −1/2 |0〉NS ⊗ b j
−1/2 |0〉NS, (4.124)
˜ b i −1/2 |0〉NS ⊗ |+〉R, (4.125)
|−〉R ⊗ b i −1/2 |0〉NS. (4.126)
The states are very similar to the ones of the type IIB string except that
now the fermionic states come with two different chiralities.
The massless spectrum of each of the type II closed-string theories contains
two Majorana–Weyl gravitinos, and therefore they form N = 2 supergravity
multiplets. Each of the states in these multiplets plays an important role in
the theory. There are 64 states in each of the four massless sectors, that we
summarize below.
• NS–NS sector: This sector is the same for the type IIA and type IIB
cases. The spectrum contains a scalar called the dilaton (one state), an
antisymmetric two-form gauge field (28 states) and a symmetric traceless
rank-two tensor, the graviton (35 states).
• NS–R and R–NS sectors: Each of these sectors contains a spin 3/2 gravitino
(56 states) and a spin 1/2 fermion called the dilatino (eight states).
In the IIB case the two gravitinos have the same chirality, whereas in the
type IIA case they have opposite chirality.
• R–R sector: These states are bosons obtained by tensoring a pair of
Majorana–Weyl spinors. In the IIA case, the two Majorana–Weyl spinors
have opposite chirality, and one obtains a one-form (vector) gauge field