String Theory Demystified

CHAPTER 12 Heterotic String Theory 215
Or it can be a fermionic state, since we need to consider the λ A as well:
A B
left = λ λ − −
12 12 0
/ /
For right movers, with N R = 0 , we can have a bosonic state:
Or a fermionic state
L (12.30)
right = i R (12.31)
a R (12.32)
Now let’s consider the case when the left movers are in the bosonic state
[Eq. (12.29)]. The bosonic sector is given by the tensor product with the
bosonic states of the right movers [Eq. (12.31)]:
j
ψ = α0
⊗ i 1 (12.33)
−
L R
The states [Eq. (12.33)] can be summarized as follows. The “particle” spectrum
includes:
• A scalar, the dilaton
j
• An antisymmetric tensor state given by α −1 0 ⊗
L
i
i
−α R −1
0 ⊗ j
j
• The graviton which is the state α 0 ⊗ i
i
+ α
0 ⊗ j
−1 L R −1
L R
L R
Now let’s take a look at the fermionic sector for the massless states. We can get
this by pairing up the bosonic states from the left movers with the fermionic states
from the right movers. This is going to give us the superpartners of Eq. (12.23). The
states can be written as
j
ψ = α
⊗ a
(12.34)
−1
0
L R
The “particle” states here include
• The superpartner of the dilaton, the dilatino
• The superpartner of the graviton, the gravitino
As you might guess from looking at the particle spectrum, supersymmetry is a
vital component of string theory. If particle accelerators never fi nd evidence of