String Theory Demystified

CHAPTER 11 Type II String Theories 201
This is a 32-component SO(10) spinor. It acts like a supercharge, taking the bosonic
a
:
state 0 NS to the fermionic state 0 R
a
a
0 = S 0
(11.21)
R
Now we have everything in place to describe the differences between type II A and
type II B string theories.
NS
Type II A String Theory
The key aspect of type II A string theory that should stick in your mind which
distinguishes it from type II B string theory is opposite chirality. That is, for a state
R ⊗ R 1 2
R and R will have opposite chirality.
1 2
First, let’s note that the total fock space is constructed as follows. First, we form
direct sums:
Then we form the tensor product:
( NS ⊕ R ) ( NS ⊕ R )
left right
( NS ⊕ R ) ⊗ ( NS ⊕ R )
left right
The physical state space is constructed using GSO projection, which will cure
the odd problem of the states differing as being fermions or bosons in space-time
and on the worldsheet described earlier, as well as allowing us to remove tachyons
from the theory. First, we construct an operator which will count up the number of
µ
excitations in a state:
d− n
∞
∑
n=
1
F = d ⋅ d
−n
n
(11.22)
It is easy to see that ( −1) F µ
tells us if a state has an even or odd number of d−n µ
excitations. Now suppose that ψ is a state with an even number of d0