Lectures on String Theory

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that of Type IIB supergravity in ten dimensions. In particular, 35 v are on-shell
degrees of freedom of the graviton, two 28 are two anisymmetric tensor fields and
35 s is a rank four antisymmetric self-dual tensor. In addition one has two real scalars.
The fermionic degrees of freedom are two spin-3/2 gravitinos, 56 c , and two spin-1/2
fermions. The presence of two gravitinos indicates that the corresponding theory
has N = 2 supersymmetry. Since the gravitions and the fermions are of the same
chirality this theory is chiral.
One can make another choice of the GSO projection by requiring that G = −Ḡ = 1.
This gives the following massless spectrum
]
]
Bosons :
[(1) + (28) + (35) v +
[(8) v + (56) v
]
]
Fermions :
[(8) c + (56) c +
[(8) s + (56) s .
There are on-shell degrees of freedom of the graviton (35 v ), antisymmetric rank three
tensor (56 v ), an antisymmetric rank two tensor (28), one vector 8 v ) and one real
scalar, which is called dilaton. The fermionic degrees of freedom comprise two spin-
3/2 gravitinos and two spin-1/2 fermions. Gravitions and fermions are of opposite
chirality. Thus, this theory has N = 2 supersymmetry also but it is non-chiral. This
string theory is called Type IIA, and the corresponding supergravity is Type IIA
supergravity.